Edit Profile (opens in new tab) Poonen, Bjorn Co-Author Distance Author ID: poonen.bjorn Published as: Poonen, Bjorn; Poonen, B.; Poonen, Björn more...less Homepage: https://math.mit.edu/~poonen/ External Links: MGP · Wikidata · GND · IdRef · theses.fr Documents Indexed: 137 Publications since 1988, including 4 Books and 12 Additional arXiv Preprints 6 Contributions as Editor · 1 Further Contribution Reviewing Activity: 13 Reviews Biographic References: 1 Publication Co-Authors: 115 Co-Authors with 80 Joint Publications 3,445 Co-Co-Authors all top 5 Co-Authors 63 single-authored 7 Stoll, Michael 5 Belabas, Karim 5 Coffman, Edward Grady jun. 5 Jordan, Bruce W. 4 Kedlaya, Kiran Sridhara 4 Rains, Eric M. 4 Rodriguez-Villegas, Fernando 3 Elkies, Noam David 3 Flatto, Leopold 3 Howe, Everett W. 3 Rubinstein, Michael O. 3 Schaefer, Edward F. 2 Baker, Matthew H. 2 Bhargava, Manjul 2 Buium, Alexandru 2 Calderbank, Arthur Robert 2 Charles, François 2 Colliot-Thélène, Jean-Louis 2 Cruz-Filipe, Luís 2 Davenport, James Harold 2 Helfgott, Harald Andrés 2 Keeton, Allan G. 2 Lagarias, Jeffrey C. 2 Leprévost, Franck 2 Maynard, James 2 McCallum, William G. 2 Pop, Florian 2 Shlapentokh, Alexandra 2 Slavov, Kaloyan 2 Tiep Pham Huu 2 Vakil, Ravi 2 Voight, John Michael 2 Voloch, José Felipe 2 Wetherell, Joseph L. 2 Zieve, Michael E. 1 Anderson, Jacqueline 1 Balakrishnan, Jennifer S. 1 Bary-Soroker, Lior 1 Berg, Jennifer 1 Berry, Neil 1 Beukers, Frits 1 Bleher, Frauke M. 1 Brock, Bradley W. 1 Bruin, Nils 1 Chinburg, Ted 1 Conrey, John Brian 1 Costa, Edgar 1 de Melo, Welington 1 Dembo, Amir 1 Doyle, John R. 1 Dubickas, Artūras 1 Duursma, Iwan Maynard 1 Epstein, Adam Lawrence 1 Fan, C. Kenneth 1 Feldmann, Anja 1 Flynn, Eugene Victor 1 Gaudry, Pierrick 1 Gonzáles, Josep 1 González-Jiménez, Enrique 1 Granville, Andrew James 1 Hamblen, Spencer 1 Hassett, Brendan 1 Hokken, David 1 Hrushovski, Ehud 1 Jarden, Moshe 1 Jelenković jun., Predrag 1 Kahale, Nabil 1 Kane, Daniel M. 1 Katz, Nicholas Michael 1 Klagsbrun, Zev 1 Kozma, Gady 1 Kresch, Andrew 1 Landesman, Aaron 1 Lenstra, Hendrik W. jun. 1 Li, Wanlin 1 Li, Wen-Ch’ing Winnie 1 Loeser, François 1 Mallows, Colin Lingwood 1 Maulik, Davesh 1 McGuire, Gary 1 Miller, Russell G. 1 Odlyzko, Andrew M. 1 Pagano, Carlo 1 Park, Jennifer 1 Plaxton, C. Greg 1 Poonen, George 1 Quasterl, Jeremy 1 Rybakov, Sergeĭ Yur’evich 1 Scholl, Anthony James 1 Schoutens, Hans 1 Shao, Qi-Man 1 Shepherd-Barron, Nicholas Ian 1 Siksek, Samir 1 Skinner, Christopher M. 1 Smyth, Christopher J. 1 Soundararajan, Kannan 1 Suel, Torsten 1 Sutherland, Andrew V. 1 Symonds, Peter 1 Tate, John Torrence jun. ...and 17 more Co-Authors all top 5 Serials 10 Mathematical Research Letters 7 Duke Mathematical Journal 7 Journal of the American Mathematical Society 6 Compositio Mathematica 5 IMRN. International Mathematics Research Notices 5 Annals of Mathematics. Second Series 4 Bulletin of the London Mathematical Society 4 Oberwolfach Reports 3 Acta Arithmetica 3 L’Enseignement Mathématique. 2e Série 3 Journal of the European Mathematical Society (JEMS) 2 American Mathematical Monthly 2 IEEE Transactions on Information Theory 2 Mathematics Magazine 2 American Journal of Mathematics 2 Journal of Algebra 2 Journal für die Reine und Angewandte Mathematik 2 Mathematische Annalen 2 Notices of the American Mathematical Society 2 Experimental Mathematics 2 Journal of Algebraic Geometry 2 Journal de Théorie des Nombres de Bordeaux 2 AMS/MAA Problem Books 1 Annales de l’Institut Fourier 1 Commentarii Mathematici Helvetici 1 The Fibonacci Quarterly 1 Inventiones Mathematicae 1 Journal of Combinatorial Theory. Series A 1 Journal of Number Theory 1 The Journal of Symbolic Logic 1 Mathematische Zeitschrift 1 Theoretical Computer Science 1 Journal of Algorithms 1 Ergodic Theory and Dynamical Systems 1 Probability Theory and Related Fields 1 Algorithmica 1 SIAM Journal on Discrete Mathematics 1 Forum Mathematicum 1 Journal of the Ramanujan Mathematical Society 1 The Annals of Applied Probability 1 Bulletin of the American Mathematical Society. New Series 1 Comptes Rendus de l’Académie des Sciences. Série I 1 SIAM Journal on Optimization 1 Journal of Mathematical Sciences (New York) 1 Finite Fields and their Applications 1 Documenta Mathematica 1 Comptes Rendus de l’Académie des Sciences. Série I. Mathématique 1 Probability in the Engineering and Informational Sciences 1 The Quarterly Journal of Mathematics 1 Graduate Studies in Mathematics 1 Progress in Mathematics 1 Panoramas et Synthèses 1 Forum of Mathematics, Sigma 1 Cambridge Journal of Mathematics 1 Simons Symposia 1 Tunisian Journal of Mathematics all top 5 Fields 104 Number theory (11-XX) 81 Algebraic geometry (14-XX) 12 Mathematical logic and foundations (03-XX) 8 General and overarching topics; collections (00-XX) 8 Field theory and polynomials (12-XX) 8 Dynamical systems and ergodic theory (37-XX) 6 Computer science (68-XX) 4 Combinatorics (05-XX) 4 Group theory and generalizations (20-XX) 3 Commutative algebra (13-XX) 3 Convex and discrete geometry (52-XX) 3 Probability theory and stochastic processes (60-XX) 3 Information and communication theory, circuits (94-XX) 2 Category theory; homological algebra (18-XX) 2 Real functions (26-XX) 2 Geometry (51-XX) 2 Operations research, mathematical programming (90-XX) 2 Mathematics education (97-XX) 1 History and biography (01-XX) 1 Order, lattices, ordered algebraic structures (06-XX) 1 General algebraic systems (08-XX) 1 Associative rings and algebras (16-XX) 1 \(K\)-theory (19-XX) 1 Topological groups, Lie groups (22-XX) 1 Functions of a complex variable (30-XX) 1 Potential theory (31-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 General topology (54-XX) 1 Numerical analysis (65-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 113 Publications have been cited 1,829 times in 1,454 Documents Cited by ▼ Year ▼ Bertini theorems over finite fields. Zbl 1084.14026 Poonen, Bjorn 85 2005 Rational points on varieties. Zbl 1387.14004 Poonen, Bjorn 84 2017 The Cassels-Tate pairing on polarized Abelian varieties. Zbl 1024.11040 Poonen, Bjorn; Stoll, Michael 76 1999 Cycles of quadratic polynomials and rational points on a genus-2 curve. Zbl 0958.11024 Flynn, E. V.; Poonen, Bjorn; Schaefer, Edward F. 55 1997 Zeros of polynomials with \(0, 1\) coefficients. Zbl 0814.30006 Odlyzko, A. M.; Poonen, B. 51 1993 Explicit descent for Jacobians of cyclic covers of the projective line. Zbl 0888.11023 Poonen, Bjorn; Schaefer, Edward F. 50 1997 Squarefree values of multivariable polynomials. Zbl 1047.11021 Poonen, Bjorn 49 2003 The method of Chabauty and Coleman. Zbl 1377.11077 McCallum, William; Poonen, Bjorn 48 2012 Large torsion subgroups of split Jacobians of curves of genus two or three. Zbl 0983.11037 Howe, Everett W.; Leprévost, Franck; Poonen, Bjorn 46 2000 The classification of rational preperiodic points of quadratic polynomials over \(\mathbb{Q}\): A refined conjecture. Zbl 0902.11025 Poonen, Bjorn 46 1998 Random maximal isotropic subspaces and Selmer groups. Zbl 1294.11097 Poonen, Bjorn; Rains, Eric 40 2012 Isomorphism types of commutative algebras of finite rank over an algebraic closed field. Zbl 1155.13015 Poonen, Bjorn 40 2008 Twists of \(X(7)\) and primitive solutions to \(x^2+y^3=z^7\). Zbl 1124.11019 Poonen, Bjorn; Schaefer, Edward F.; Stoll, Michael 39 2007 A computable functor from graphs to fields. Zbl 1447.03005 Miller, Russell; Poonen, Bjorn; Schoutens, Hans; Shlapentokh, Alexandra 38 2018 Finiteness results for modular curves of genus at least 2. Zbl 1127.11041 Baker, Matthew H.; González-Jiménez, Enrique; Gonzáles, Josep; Poonen, Bjorn 36 2005 Maximally complete fields. Zbl 0807.12006 Poonen, Bjorn 33 1993 Local height functions and the Mordell-Weil theorem for Drinfeld modules. Zbl 0839.11024 Poonen, Bjorn 31 1995 A heuristic for boundedness of ranks of elliptic curves. Zbl 1469.11173 Park, Jennifer; Poonen, Bjorn; Voight, John; Wood, Melanie Matchett 31 2019 Using elliptic curves of rank one towards the undecidability of Hilbert’s tenth problem over rings of algebraic integers. Zbl 1057.11068 Poonen, Bjorn 30 2002 Union-closed families. Zbl 0758.05096 Poonen, Bjorn 30 1992 Hilbert’s Tenth Problem and Mazur’s Conjecture for large subrings of \(\mathbb{Q}\). Zbl 1028.11077 Poonen, Bjorn 29 2003 The Grothendieck ring of varieties is not a domain. Zbl 1054.14505 Poonen, Bjorn 28 2002 Insufficiency of the Brauer-Manin obstruction applied to étale covers. Zbl 1284.11096 Poonen, Bjorn 27 2010 Modeling the distribution of ranks, Selmer groups, and Shafarevich-Tate groups of elliptic curves. Zbl 1329.14071 Bhargava, Manjul; Kane, Daniel M.; Lenstra, Hendrik W. jun.; Poonen, Bjorn; Rains, Eric 25 2015 Random polynomials having few or no real zeros. Zbl 1002.60045 Dembo, Amir; Poonen, Bjorn; Shao, Qi-Man; Zeitouni, Ofer 25 2002 Gonality of modular curves in characteristic \(p\). Zbl 1138.14016 Poonen, Bjorn 24 2007 Random Diophantine equations. With appendices by Jean-Louis Colliot-Thélène and Nicholas M. Katz. Zbl 1208.11050 Poonen, Bjorn; Voloch, José Felipe 24 2004 Mordell-Lang plus Bogomolov. Zbl 0995.11040 Poonen, Bjorn 23 1999 Generalized explicit descent and its application to curves of genus 3. Zbl 1408.11065 Bruin, Nils; Poonen, Bjorn; Stoll, Michael 23 2016 Heuristics for the Brauer-Manin obstruction for curves. Zbl 1173.11040 Poonen, Bjorn 22 2006 Néron-Severi groups under specialization. Zbl 1248.14011 Maulik, Davesh; Poonen, Bjorn 21 2012 The zeta function of the beta transformation. Zbl 0843.58106 Flatto, Leopold; Lagarias, Jeffrey C.; Poonen, Bjorn 21 1994 The Brauer-Manin obstruction for subvarieties of abelian varieties over function fields. Zbl 1294.11110 Poonen, Bjorn; Voloch, José Felipe 20 2010 Algebraic families of nonzero elements of Shafarevich-Tate groups. Zbl 0951.11022 Colliot-Thélène, Jean-Louis; Poonen, Bjorn 19 2000 Zeros of Fekete polynomials. Zbl 1007.11053 Conrey, Brian; Granville, Andrew; Poonen, Bjorn; Soundararajan, K. 19 2000 The moduli space of commutative algebras of finite rank. Zbl 1151.14011 Poonen, Bjorn 19 2008 Independence of points on elliptic curves arising from special points on modular and Shimura curves. II: Local results. Zbl 1232.11073 Buium, Alexandru; Poonen, Bjorn 18 2009 Characterizing integers among rational numbers with a universal-existential formula. Zbl 1179.11047 Poonen, Bjorn 18 2009 Lattice polygons and the number 12. Zbl 0988.52024 Poonen, Bjorn; Rodriguez-Villegas, Fernando 18 2000 Existence of rational points on smooth projective varieties. Zbl 1183.14032 Poonen, Bjorn 17 2009 The number of intersection points made by the diagonals of a regular polygon. Zbl 0913.51005 Poonen, Bjorn; Rubinstein, Michael 16 1998 Packing random intervals on-line. Zbl 0914.68082 Coffman, E. G. jun.; Flatto, L.; Jelenković, P.; Poonen, B. 16 1998 Undecidability in number theory. Zbl 1194.03018 Poonen, Bjorn 16 2008 Bertini irreducibility theorems over finite fields. Zbl 1327.14233 Charles, François; Poonen, Bjorn 15 2016 Most odd degree hyperelliptic curves have only one rational point. Zbl 1303.11073 Poonen, Bjorn; Stoll, Michael 15 2014 An explicit algebraic family of genus-one curves violating the Hasse principle. Zbl 1046.11038 Poonen, Bjorn 14 2001 Diophantine definability of infinite discrete nonarchimedean sets and Diophantine models over large subrings of number field. Zbl 1139.11056 Poonen, Bjorn; Shlapentokh, Alexandra 14 2005 Computing Néron-Severi groups and cycle class groups. Zbl 1316.14017 Poonen, Bjorn; Testa, Damiano; van Luijk, Ronald 14 2015 A local-global principle for densities. Zbl 1024.11047 Poonen, Bjorn; Stoll, Michael 13 1999 Berkovich spaces embed in Euclidean spaces. Zbl 1325.14040 Hrushovski, Ehud; Loeser, François; Poonen, Bjorn 13 2014 On a conjecture of Helleseth regarding pairs of binary \(m\)-sequences. Zbl 0943.94513 Calderbank, A. R.; McGuire, Gary; Poonen, Bjorn; Rubinstein, Michael 12 1996 Computational aspects of curves of genus at least 2. Zbl 0891.11037 Poonen, Bjorn 12 1996 Smooth hypersurface sections containing a given subscheme over a finite field. Zbl 1207.14047 Poonen, Bjorn 11 2008 \(p\)-adic interpolation of iterates. Zbl 1291.11135 Poonen, Bjorn 11 2014 Convergence of the restricted Nelder-Mead algorithm in two dimensions. Zbl 1246.49029 Lagarias, Jeffrey C.; Poonen, Bjorn; Wright, Margaret H. 10 2012 Some diophantine equations of the form \(x^n+y^n=z^m\). Zbl 0930.11017 Poonen, Bjorn 10 1998 Computing torsion points on curves. Zbl 1063.11017 Poonen, Bjorn 10 2001 Curves of every genus with many points. II: Asymptotically good families. Zbl 1072.11041 Elkies, Noam D.; Howe, Everett W.; Kresch, Andrew; Poonen, Bjorn; Wetherell, Joseph L.; Zieve, Michael E. 10 2004 Torsion in rank 1 Drinfeld modules and the uniform boundedness conjecture. Zbl 0891.11034 Poonen, Bjorn 9 1997 Computing rational points on curves. Zbl 1038.11037 Poonen, Bjorn 9 2002 Varieties without extra automorphisms. II: Hyperelliptic curves. Zbl 0966.14020 Poonen, Bjorn 8 2000 The conjugate dimension of algebraic numbers. Zbl 1062.11064 Berry, Neil; Dubickas, Artūras; Elkies, Noam D.; Poonen, Bjorn; Smyth, Chris 8 2004 Varieties without extra automorphisms. III: Hypersurfaces. Zbl 1076.14053 Poonen, Bjorn 8 2005 Undecidable problems: a sampler. Zbl 1358.03063 Poonen, Bjorn 8 2014 Automorphisms of Harbater-Katz-Gabber curves. Zbl 1372.14022 Bleher, Frauke M.; Chinburg, Ted; Poonen, Bjorn; Symonds, Peter 8 2017 Self cup products and the theta characteristic torsor. Zbl 1297.18005 Poonen, Bjorn; Rains, Eric 8 2011 Gonality of dynatomic curves and strong uniform boundedness of preperiodic points. Zbl 1445.37080 Doyle, John R.; Poonen, Bjorn 8 2020 Integrality and rigidity for postcritically finite polynomials. Zbl 1291.37057 Epstein, Adam 7 2012 Abelian varieties isogenous to a power of an elliptic curve. Zbl 1400.14116 Jordan, Bruce W.; Keeton, Allan G.; Poonen, Bjorn; Rains, Eric M.; Shepherd-Barron, Nicholas; Tate, John T. 7 2018 Varieties without extra automorphisms. I: Curves. Zbl 0966.14019 Poonen, Bjorn 6 2000 Packing random intervals. Zbl 0819.60013 Coffman, E. G. jun.; Poonen, Bjorn; Winkler, Peter 6 1995 First-order characterization of function field invariants over large fields. Zbl 1174.03015 Poonen, Bjorn; Pop, Florian 6 2008 A 2-adic approach to the analysis of cyclic codes. Zbl 0898.94011 Calderbank, A. R.; Li, Wen-Ching Winnie; Poonen, Bjorn 6 1997 Uniform first-order definitions in finitely generated fields. Zbl 1197.12005 Poonen, Bjorn 5 2007 Parking arcs on the circle with applications to one-dimensional communication networks. Zbl 0812.60090 Coffman, E. G. jun.; Mallows, C. L.; Poonen, Bjorn 5 1994 Independence of points on elliptic curves arising from special points on modular and Shimura curves. I: Global results. Zbl 1177.11050 Buium, Alexandru; Poonen, Bjorn 5 2009 The set of nonsquares in a number field is diophantine. Zbl 1183.14031 Poonen, Bjorn 5 2009 Heuristics for the arithmetic of elliptic curves. Zbl 1443.11100 Poonen, Bjorn 5 2018 Curves over every global field violating the local-global principle. Zbl 1294.11108 Poonen, B. 5 2010 Drinfeld modules with no supersingular primes. Zbl 0898.11024 Poonen, Bjorn 4 1998 Torsion packets on curves. Zbl 0987.14020 Baker, Matthew; Poonen, Bjorn 4 2001 Explicit methods in number theory. Rational points and Diophantine equations. Zbl 1267.11002 Belabas, Karim; Beukers, Frits; Gaudry, Pierrick; McCallum, William; Poonen, Bjorn; Siksek, Samir; Stoll, Michael; Watkins, Mark 4 2012 Using zeta functions to factor polynomials over finite fields. Zbl 1468.11247 Poonen, Bjorn 4 2019 The exceptional locus in the Bertini irreducibility theorem for a morphism. Zbl 1483.14097 Poonen, Bjorn; Slavov, Kaloyan 4 2022 Average rank of elliptic curves [after Manjul Bhargava and Arul Shankar]. Zbl 1295.11065 Poonen, Bjorn 4 2013 Periodicity of a combinatorial sequence. Zbl 0644.10012 Poonen, Bjorn 3 1988 Zeros of sparse polynomials over local fields of characteristic \(p\). Zbl 0931.11053 Poonen, Bjorn 3 1998 Unramified covers of Galois covers of low genus curves. Zbl 1082.14035 Poonen, Bjorn 3 2005 Automorphisms mapping a point into a subvariety. Zbl 1229.14032 Poonen, Bjorn 3 2011 Points having the same residue field as their image under a morphism. Zbl 1077.14505 Poonen, Bjorn 3 2001 Improved lower bounds for Shellsort. Zbl 0977.68532 Plaxton, C. Greg; Poonen, Bjorn; Suel, Torsten 3 1992 The Hasse principle for complete intersections in projective space. Zbl 1079.14027 Poonen, Bjorn 3 2001 Orbits of automorphism groups of fields. Zbl 1132.12002 Kedlaya, Kiran S.; Poonen, Bjorn 3 2005 Fractional power series and pairings on Drinfeld modules. Zbl 0861.13010 Poonen, Bjorn 3 1996 Extending self-maps to projective space over finite fields. Zbl 1303.14014 Poonen, Bjorn 3 2013 Multivariable polynomial injections on rational numbers. Zbl 1261.11030 Poonen, Bjorn 3 2010 Computing call admission capacities in linear networks. Zbl 0969.90025 Coffman, E. G. jun.; Feldmann, Anja; Kahale, Nabil; Poonen, Bjorn 2 1999 Genus-two curves with 22 torsion points. Zbl 0966.11026 Poonen, Bjorn 2 2000 Multiples of subvarieties in algebraic groups over finite fields. Zbl 1082.14028 Poonen, Bjorn 2 2005 Spans of Hecke points on modular curves. Zbl 1081.11043 Poonen, Bjorn 2 2001 The exceptional locus in the Bertini irreducibility theorem for a morphism. Zbl 1483.14097 Poonen, Bjorn; Slavov, Kaloyan 4 2022 The proportion of derangements characterizes the symmetric and alternating groups. Zbl 1522.20021 Poonen, Bjorn; Slavov, Kaloyan 1 2022 A \(p\)-adic approach to rational points on curves. Zbl 1461.11099 Poonen, Bjorn 1 2021 Arithmetic geometry, number theory, and computation. Zbl 1515.11004 1 2021 Gonality of dynatomic curves and strong uniform boundedness of preperiodic points. Zbl 1445.37080 Doyle, John R.; Poonen, Bjorn 8 2020 The analytic class number formula for 1-dimensional affine schemes. Zbl 1473.11212 Jordan, Bruce W.; Poonen, Bjorn 2 2020 A heuristic for boundedness of ranks of elliptic curves. Zbl 1469.11173 Park, Jennifer; Poonen, Bjorn; Voight, John; Wood, Melanie Matchett 31 2019 Using zeta functions to factor polynomials over finite fields. Zbl 1468.11247 Poonen, Bjorn 4 2019 A computable functor from graphs to fields. Zbl 1447.03005 Miller, Russell; Poonen, Bjorn; Schoutens, Hans; Shlapentokh, Alexandra 38 2018 Abelian varieties isogenous to a power of an elliptic curve. Zbl 1400.14116 Jordan, Bruce W.; Keeton, Allan G.; Poonen, Bjorn; Rains, Eric M.; Shepherd-Barron, Nicholas; Tate, John T. 7 2018 Heuristics for the arithmetic of elliptic curves. Zbl 1443.11100 Poonen, Bjorn 5 2018 Machine-assisted proofs. Zbl 1452.68262 Davenport, James; Poonen, Bjorn; Maynard, James; Helfgott, Harald; Tiep, Pham Huu; Cruz-Filipe, Luís 2 2018 Local arboreal representations. Zbl 1452.11140 Anderson, Jacqueline; Hamblen, Spencer; Poonen, Bjorn; Walton, Laura 2 2018 Rational points on varieties. Zbl 1387.14004 Poonen, Bjorn 84 2017 Automorphisms of Harbater-Katz-Gabber curves. Zbl 1372.14022 Bleher, Frauke M.; Chinburg, Ted; Poonen, Bjorn; Symonds, Peter 8 2017 Generalized explicit descent and its application to curves of genus 3. Zbl 1408.11065 Bruin, Nils; Poonen, Bjorn; Stoll, Michael 23 2016 Bertini irreducibility theorems over finite fields. Zbl 1327.14233 Charles, François; Poonen, Bjorn 15 2016 Galois points on varieties. Zbl 1425.11132 Jarden, Moshe; Poonen, Bjorn 1 2016 Modeling the distribution of ranks, Selmer groups, and Shafarevich-Tate groups of elliptic curves. Zbl 1329.14071 Bhargava, Manjul; Kane, Daniel M.; Lenstra, Hendrik W. jun.; Poonen, Bjorn; Rains, Eric 25 2015 Computing Néron-Severi groups and cycle class groups. Zbl 1316.14017 Poonen, Bjorn; Testa, Damiano; van Luijk, Ronald 14 2015 Most odd degree hyperelliptic curves have only one rational point. Zbl 1303.11073 Poonen, Bjorn; Stoll, Michael 15 2014 Berkovich spaces embed in Euclidean spaces. Zbl 1325.14040 Hrushovski, Ehud; Loeser, François; Poonen, Bjorn 13 2014 \(p\)-adic interpolation of iterates. Zbl 1291.11135 Poonen, Bjorn 11 2014 Undecidable problems: a sampler. Zbl 1358.03063 Poonen, Bjorn 8 2014 Average rank of elliptic curves [after Manjul Bhargava and Arul Shankar]. Zbl 1295.11065 Poonen, Bjorn 4 2013 Extending self-maps to projective space over finite fields. Zbl 1303.14014 Poonen, Bjorn 3 2013 The method of Chabauty and Coleman. Zbl 1377.11077 McCallum, William; Poonen, Bjorn 48 2012 Random maximal isotropic subspaces and Selmer groups. Zbl 1294.11097 Poonen, Bjorn; Rains, Eric 40 2012 Néron-Severi groups under specialization. Zbl 1248.14011 Maulik, Davesh; Poonen, Bjorn 21 2012 Convergence of the restricted Nelder-Mead algorithm in two dimensions. Zbl 1246.49029 Lagarias, Jeffrey C.; Poonen, Bjorn; Wright, Margaret H. 10 2012 Integrality and rigidity for postcritically finite polynomials. Zbl 1291.37057 Epstein, Adam 7 2012 Explicit methods in number theory. Rational points and Diophantine equations. Zbl 1267.11002 Belabas, Karim; Beukers, Frits; Gaudry, Pierrick; McCallum, William; Poonen, Bjorn; Siksek, Samir; Stoll, Michael; Watkins, Mark 4 2012 Self cup products and the theta characteristic torsor. Zbl 1297.18005 Poonen, Bjorn; Rains, Eric 8 2011 Automorphisms mapping a point into a subvariety. Zbl 1229.14032 Poonen, Bjorn 3 2011 Insufficiency of the Brauer-Manin obstruction applied to étale covers. Zbl 1284.11096 Poonen, Bjorn 27 2010 The Brauer-Manin obstruction for subvarieties of abelian varieties over function fields. Zbl 1294.11110 Poonen, Bjorn; Voloch, José Felipe 20 2010 Curves over every global field violating the local-global principle. Zbl 1294.11108 Poonen, B. 5 2010 Multivariable polynomial injections on rational numbers. Zbl 1261.11030 Poonen, Bjorn 3 2010 Independence of points on elliptic curves arising from special points on modular and Shimura curves. II: Local results. Zbl 1232.11073 Buium, Alexandru; Poonen, Bjorn 18 2009 Characterizing integers among rational numbers with a universal-existential formula. Zbl 1179.11047 Poonen, Bjorn 18 2009 Existence of rational points on smooth projective varieties. Zbl 1183.14032 Poonen, Bjorn 17 2009 Independence of points on elliptic curves arising from special points on modular and Shimura curves. I: Global results. Zbl 1177.11050 Buium, Alexandru; Poonen, Bjorn 5 2009 The set of nonsquares in a number field is diophantine. Zbl 1183.14031 Poonen, Bjorn 5 2009 Isomorphism types of commutative algebras of finite rank over an algebraic closed field. Zbl 1155.13015 Poonen, Bjorn 40 2008 The moduli space of commutative algebras of finite rank. Zbl 1151.14011 Poonen, Bjorn 19 2008 Undecidability in number theory. Zbl 1194.03018 Poonen, Bjorn 16 2008 Smooth hypersurface sections containing a given subscheme over a finite field. Zbl 1207.14047 Poonen, Bjorn 11 2008 First-order characterization of function field invariants over large fields. Zbl 1174.03015 Poonen, Bjorn; Pop, Florian 6 2008 Elliptic curves. Zbl 1214.11073 Poonen, Bjorn 1 2008 Twists of \(X(7)\) and primitive solutions to \(x^2+y^3=z^7\). Zbl 1124.11019 Poonen, Bjorn; Schaefer, Edward F.; Stoll, Michael 39 2007 Gonality of modular curves in characteristic \(p\). Zbl 1138.14016 Poonen, Bjorn 24 2007 Uniform first-order definitions in finitely generated fields. Zbl 1197.12005 Poonen, Bjorn 5 2007 Sieve methods for varieties over finite fields and arithmetic schemes. Zbl 1149.11031 Poonen, Bjorn 1 2007 Heuristics for the Brauer-Manin obstruction for curves. Zbl 1173.11040 Poonen, Bjorn 22 2006 Bertini theorems over finite fields. Zbl 1084.14026 Poonen, Bjorn 85 2005 Finiteness results for modular curves of genus at least 2. Zbl 1127.11041 Baker, Matthew H.; González-Jiménez, Enrique; Gonzáles, Josep; Poonen, Bjorn 36 2005 Diophantine definability of infinite discrete nonarchimedean sets and Diophantine models over large subrings of number field. Zbl 1139.11056 Poonen, Bjorn; Shlapentokh, Alexandra 14 2005 Varieties without extra automorphisms. III: Hypersurfaces. Zbl 1076.14053 Poonen, Bjorn 8 2005 Unramified covers of Galois covers of low genus curves. Zbl 1082.14035 Poonen, Bjorn 3 2005 Orbits of automorphism groups of fields. Zbl 1132.12002 Kedlaya, Kiran S.; Poonen, Bjorn 3 2005 Multiples of subvarieties in algebraic groups over finite fields. Zbl 1082.14028 Poonen, Bjorn 2 2005 Random Diophantine equations. With appendices by Jean-Louis Colliot-Thélène and Nicholas M. Katz. Zbl 1208.11050 Poonen, Bjorn; Voloch, José Felipe 24 2004 Curves of every genus with many points. II: Asymptotically good families. Zbl 1072.11041 Elkies, Noam D.; Howe, Everett W.; Kresch, Andrew; Poonen, Bjorn; Wetherell, Joseph L.; Zieve, Michael E. 10 2004 The conjugate dimension of algebraic numbers. Zbl 1062.11064 Berry, Neil; Dubickas, Artūras; Elkies, Noam D.; Poonen, Bjorn; Smyth, Chris 8 2004 Arithmetic of higher-dimensional algebraic varieties. Proceedings of the workshop on rational and integral points of higher-dimensional varieties, Palo Alto, CA, USA, December 11–20, 2002. Zbl 1054.11006 2 2004 Squarefree values of multivariable polynomials. Zbl 1047.11021 Poonen, Bjorn 49 2003 Hilbert’s Tenth Problem and Mazur’s Conjecture for large subrings of \(\mathbb{Q}\). Zbl 1028.11077 Poonen, Bjorn 29 2003 Using elliptic curves of rank one towards the undecidability of Hilbert’s tenth problem over rings of algebraic integers. Zbl 1057.11068 Poonen, Bjorn 30 2002 The Grothendieck ring of varieties is not a domain. Zbl 1054.14505 Poonen, Bjorn 28 2002 Random polynomials having few or no real zeros. Zbl 1002.60045 Dembo, Amir; Poonen, Bjorn; Shao, Qi-Man; Zeitouni, Ofer 25 2002 Computing rational points on curves. Zbl 1038.11037 Poonen, Bjorn 9 2002 The William Lowell Putnam mathematical competition 1985–2000. Problems, solutions, and commentary. Zbl 1005.00003 Kedlaya, Kiran S.; Poonen, Bjorn; Vakil, Ravi 1 2002 An explicit algebraic family of genus-one curves violating the Hasse principle. Zbl 1046.11038 Poonen, Bjorn 14 2001 Computing torsion points on curves. Zbl 1063.11017 Poonen, Bjorn 10 2001 Torsion packets on curves. Zbl 0987.14020 Baker, Matthew; Poonen, Bjorn 4 2001 Points having the same residue field as their image under a morphism. Zbl 1077.14505 Poonen, Bjorn 3 2001 The Hasse principle for complete intersections in projective space. Zbl 1079.14027 Poonen, Bjorn 3 2001 Spans of Hecke points on modular curves. Zbl 1081.11043 Poonen, Bjorn 2 2001 Large torsion subgroups of split Jacobians of curves of genus two or three. Zbl 0983.11037 Howe, Everett W.; Leprévost, Franck; Poonen, Bjorn 46 2000 Algebraic families of nonzero elements of Shafarevich-Tate groups. Zbl 0951.11022 Colliot-Thélène, Jean-Louis; Poonen, Bjorn 19 2000 Zeros of Fekete polynomials. Zbl 1007.11053 Conrey, Brian; Granville, Andrew; Poonen, Bjorn; Soundararajan, K. 19 2000 Lattice polygons and the number 12. Zbl 0988.52024 Poonen, Bjorn; Rodriguez-Villegas, Fernando 18 2000 Varieties without extra automorphisms. II: Hyperelliptic curves. Zbl 0966.14020 Poonen, Bjorn 8 2000 Varieties without extra automorphisms. I: Curves. Zbl 0966.14019 Poonen, Bjorn 6 2000 Genus-two curves with 22 torsion points. Zbl 0966.11026 Poonen, Bjorn 2 2000 The Cassels-Tate pairing on polarized Abelian varieties. Zbl 1024.11040 Poonen, Bjorn; Stoll, Michael 76 1999 Mordell-Lang plus Bogomolov. Zbl 0995.11040 Poonen, Bjorn 23 1999 A local-global principle for densities. Zbl 1024.11047 Poonen, Bjorn; Stoll, Michael 13 1999 Computing call admission capacities in linear networks. Zbl 0969.90025 Coffman, E. G. jun.; Feldmann, Anja; Kahale, Nabil; Poonen, Bjorn 2 1999 The classification of rational preperiodic points of quadratic polynomials over \(\mathbb{Q}\): A refined conjecture. Zbl 0902.11025 Poonen, Bjorn 46 1998 The number of intersection points made by the diagonals of a regular polygon. Zbl 0913.51005 Poonen, Bjorn; Rubinstein, Michael 16 1998 Packing random intervals on-line. Zbl 0914.68082 Coffman, E. G. jun.; Flatto, L.; Jelenković, P.; Poonen, B. 16 1998 Some diophantine equations of the form \(x^n+y^n=z^m\). Zbl 0930.11017 Poonen, Bjorn 10 1998 Drinfeld modules with no supersingular primes. Zbl 0898.11024 Poonen, Bjorn 4 1998 Zeros of sparse polynomials over local fields of characteristic \(p\). Zbl 0931.11053 Poonen, Bjorn 3 1998 Cycles of quadratic polynomials and rational points on a genus-2 curve. Zbl 0958.11024 Flynn, E. V.; Poonen, Bjorn; Schaefer, Edward F. 55 1997 Explicit descent for Jacobians of cyclic covers of the projective line. Zbl 0888.11023 Poonen, Bjorn; Schaefer, Edward F. 50 1997 Torsion in rank 1 Drinfeld modules and the uniform boundedness conjecture. Zbl 0891.11034 Poonen, Bjorn 9 1997 A 2-adic approach to the analysis of cyclic codes. Zbl 0898.94011 Calderbank, A. R.; Li, Wen-Ching Winnie; Poonen, Bjorn 6 1997 On a conjecture of Helleseth regarding pairs of binary \(m\)-sequences. Zbl 0943.94513 Calderbank, A. R.; McGuire, Gary; Poonen, Bjorn; Rubinstein, Michael 12 1996 ...and 13 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 1,564 Authors 36 Poonen, Bjorn 20 Stoll, Michael 18 Shlapentokh, Alexandra 15 Miller, Russell G. 14 Creutz, Brendan 14 Fisher, Tom A. 12 Pasten, Hector V. 12 Viray, Bianca 12 Voloch, José Felipe 11 Balakrishnan, Jennifer S. 11 Bhargava, Manjul 11 Flynn, Eugene Victor 11 Ghioca, Dragos 11 Kedlaya, Kiran Sridhara 11 Loughran, Daniel 10 Buium, Alexandru 10 Doyle, John R. 10 Erdélyi, Tamás 9 Bazhenov, Nikolaĭ Alekseevich 9 Howe, Everett W. 9 Siksek, Samir 8 Gonzalez Rovira, Josep 8 Lorenzo García, Elisa 8 Mazur, Barry 8 Ritzenthaler, Christophe 8 Wood, Melanie Matchett 7 Asgarli, Shamil 7 Borwein, Peter Benjamin 7 Cornelissen, Gunther 7 Ishitsuka, Yasuhiro 7 Katz, Daniel J. 7 Li, Wanlin 7 Liu, Qing 7 Müller, Jan Steffen 7 Silverman, Joseph Hillel 6 Browning, Timothy Daniel 6 Bruin, Nils 6 Cao, Yang 6 Colliot-Thélène, Jean-Louis 6 Cremona, John E. 6 Freitas, Nuno 6 Harrison-Trainor, Matthew 6 Ingram, Patrick 6 Liang, Yongqi 6 Rojas, J. Maurice 6 Schaefer, Edward F. 6 Shparlinski, Igor E. 6 Várilly-Alvarado, Anthony 5 Bars Cortina, Francesc 5 Bennett, Michael A. 5 Berenhaut, Kenneth S. 5 Castryck, Wouter 5 Elias, Joan 5 Faber, Xander 5 Fehm, Arno 5 Hindes, Wade 5 Ito, Tetsushi 5 Knight, Julia F. 5 Krumm, David 5 Langevin, Philippe 5 Lorenzini, Dino J. 5 Manes, Michelle 5 Melnikov, Alexander G. 5 Micheli, Giacomo 5 Nakahara, Masahiro 5 Pries, Rachel J. 5 Rubin, Karl Cooper 5 Sijsling, Jeroen 5 Sutherland, Andrew V. 5 Voight, John Michael 5 Wang, Xiaoheng 5 Wu, Han 5 Xue, Jiangwei 5 Zarkhin, Yuriĭ Gennad’evich 5 Zureick-Brown, David 4 Baryshnikov, Yuliy M. 4 Benedetto, Robert L. 4 Bruhn, Henning 4 Casnati, Gianfranco 4 Česnavičius, Kęstutis 4 Clark, Peter Louis 4 David, Chantal 4 Dembo, Amir 4 Dokchitser, Vladimir 4 Dujella, Andrej 4 Favre, Charles 4 González-Jiménez, Enrique 4 Habegger, Philipp 4 Hare, Kevin G. 4 Hirakawa, Yoshinosuke 4 Ho, Wei 4 Homs Pons, Roser 4 Hutz, Benjamin 4 Ieronymou, Evis 4 Joshi, Vinayak V. 4 Kaplan, Nathan 4 Keller, Timo 4 König, Joachim 4 Le Boudec, Pierre 4 Panin, Ivan A. ...and 1,464 more Authors all top 5 Cited in 260 Serials 106 Journal of Number Theory 52 Mathematics of Computation 45 Transactions of the American Mathematical Society 43 Journal de Théorie des Nombres de Bordeaux 42 Advances in Mathematics 40 Journal of Algebra 35 Compositio Mathematica 34 International Journal of Number Theory 33 Mathematische Annalen 33 Proceedings of the American Mathematical Society 30 Duke Mathematical Journal 28 Research in Number Theory 25 Journal of Pure and Applied Algebra 23 Algebra & Number Theory 20 Manuscripta Mathematica 19 Mathematical Proceedings of the Cambridge Philosophical Society 19 Acta Arithmetica 18 Annals of Mathematics. Second Series 17 Mathematische Zeitschrift 16 Inventiones Mathematicae 15 The Journal of Symbolic Logic 15 Finite Fields and their Applications 15 Journal of the European Mathematical Society (JEMS) 14 Bulletin of the London Mathematical Society 13 Annales de l’Institut Fourier 12 Journal für die Reine und Angewandte Mathematik 12 Experimental Mathematics 11 LMS Journal of Computation and Mathematics 11 Journal of the Institute of Mathematics of Jussieu 10 Rocky Mountain Journal of Mathematics 10 Journal of the London Mathematical Society. Second Series 10 Journal of Symbolic Computation 10 Journal of the American Mathematical Society 10 Bulletin of the American Mathematical Society. New Series 10 The Ramanujan Journal 9 Communications in Algebra 9 Monatshefte für Mathematik 9 Journal of Mathematical Sciences (New York) 8 Israel Journal of Mathematics 8 Michigan Mathematical Journal 8 Proceedings of the London Mathematical Society. Third Series 8 Comptes Rendus. Mathématique. Académie des Sciences, Paris 8 Forum of Mathematics, Sigma 7 Discrete Mathematics 7 Algebra and Logic 7 Journal of Combinatorial Theory. Series A 7 Mathematika 7 The Annals of Applied Probability 7 Indagationes Mathematicae. New Series 7 The Electronic Journal of Combinatorics 6 Memoirs of the American Mathematical Society 6 Annals of Pure and Applied Logic 6 Forum Mathematicum 6 Linear Algebra and its Applications 6 Selecta Mathematica. New Series 6 Integers 6 European Journal of Mathematics 5 Bulletin of the Australian Mathematical Society 5 Bulletin de la Société Mathématique de France 5 Nagoya Mathematical Journal 5 Journal of the Ramanujan Mathematical Society 5 Journal of Algebraic Geometry 5 Documenta Mathematica 5 Research in the Mathematical Sciences 4 Journal of Statistical Physics 4 The Annals of Probability 4 Archiv der Mathematik 4 Commentarii Mathematici Helvetici 4 Functiones et Approximatio. Commentarii Mathematici 4 Mathematische Nachrichten 4 European Journal of Combinatorics 4 Ergodic Theory and Dynamical Systems 4 Discrete & Computational Geometry 4 Revista Matemática Iberoamericana 4 SIAM Journal on Discrete Mathematics 4 Designs, Codes and Cryptography 4 Annales de l’Institut Henri Poincaré. Probabilités et Statistiques 4 The New York Journal of Mathematics 4 Bulletin des Sciences Mathématiques 4 Acta Mathematica Sinica. English Series 4 Journal of the Australian Mathematical Society 4 Forum of Mathematics, Pi 3 Communications in Mathematical Physics 3 Journal d’Analyse Mathématique 3 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 3 Canadian Mathematical Bulletin 3 Illinois Journal of Mathematics 3 Probability Theory and Related Fields 3 International Journal of Algebra and Computation 3 IMRN. International Mathematics Research Notices 3 The Journal of Geometric Analysis 3 Stochastic Processes and their Applications 3 Expositiones Mathematicae 3 Archive for Mathematical Logic 3 Applicable Algebra in Engineering, Communication and Computing 3 Journal of Algebraic Combinatorics 3 Izvestiya: Mathematics 3 Transformation Groups 3 Algebraic & Geometric Topology 3 Foundations of Computational Mathematics ...and 160 more Serials all top 5 Cited in 54 Fields 891 Number theory (11-XX) 729 Algebraic geometry (14-XX) 98 Mathematical logic and foundations (03-XX) 95 Dynamical systems and ergodic theory (37-XX) 80 Field theory and polynomials (12-XX) 79 Combinatorics (05-XX) 76 Commutative algebra (13-XX) 69 Probability theory and stochastic processes (60-XX) 59 Group theory and generalizations (20-XX) 41 Functions of a complex variable (30-XX) 36 Computer science (68-XX) 32 Information and communication theory, circuits (94-XX) 27 Several complex variables and analytic spaces (32-XX) 25 Real functions (26-XX) 24 Linear and multilinear algebra; matrix theory (15-XX) 22 Associative rings and algebras (16-XX) 19 Convex and discrete geometry (52-XX) 18 Operations research, mathematical programming (90-XX) 17 Order, lattices, ordered algebraic structures (06-XX) 16 \(K\)-theory (19-XX) 15 Numerical analysis (65-XX) 14 Algebraic topology (55-XX) 13 Nonassociative rings and algebras (17-XX) 13 Geometry (51-XX) 11 Quantum theory (81-XX) 10 Harmonic analysis on Euclidean spaces (42-XX) 9 Category theory; homological algebra (18-XX) 9 Topological groups, Lie groups (22-XX) 9 Differential geometry (53-XX) 9 Manifolds and cell complexes (57-XX) 8 Statistical mechanics, structure of matter (82-XX) 6 General and overarching topics; collections (00-XX) 6 History and biography (01-XX) 6 Measure and integration (28-XX) 6 Approximations and expansions (41-XX) 6 Functional analysis (46-XX) 5 Special functions (33-XX) 5 Partial differential equations (35-XX) 3 General algebraic systems (08-XX) 3 Ordinary differential equations (34-XX) 2 Potential theory (31-XX) 2 Difference and functional equations (39-XX) 2 Operator theory (47-XX) 2 Global analysis, analysis on manifolds (58-XX) 2 Statistics (62-XX) 2 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 General topology (54-XX) 1 Mechanics of particles and systems (70-XX) 1 Fluid mechanics (76-XX) 1 Optics, electromagnetic theory (78-XX) 1 Relativity and gravitational theory (83-XX) 1 Geophysics (86-XX) 1 Biology and other natural sciences (92-XX) 1 Systems theory; control (93-XX) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. 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