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## Bruin, Nils

Compute Distance To:
 Author ID: bruin.nils Published as: Bruin, N.; Bruin, Nils
 Documents Indexed: 32 Publications since 1999
all top 5

#### Co-Authors

 8 single-authored 7 Flynn, Eugene Victor 4 Stoll, Michael 2 González, Josep R. 1 Bell, Jason P. 1 Bright, M. J. 1 Coons, Michael 1 Dahmen, Sander R. 1 Doerksen, Kevin 1 Elkies, Noam David 1 Fernandez, Julio 1 Fisher, Tom A. 1 Hemenway, Brett 1 Lario, Joan-Carles 1 Lewis, Daniel 1 Logan, Adam 1 Molnar, Alexander 1 Nasserden, Brett 1 Poonen, Bjorn 1 Rotger, Victor 1 Sertöz, Emre Can 1 Testa, Damiano
all top 5

#### Serials

 3 Acta Arithmetica 3 Transactions of the American Mathematical Society 3 LMS Journal of Computation and Mathematics 2 Mathematical Proceedings of the Cambridge Philosophical Society 2 Mathematics of Computation 2 Compositio Mathematica 2 Journal of Number Theory 1 Canadian Journal of Mathematics 1 Journal of the London Mathematical Society. Second Series 1 Journal für die Reine und Angewandte Mathematik 1 Experimental Mathematics 1 Forum of Mathematics, Sigma 1 Research in Number Theory

#### Fields

 28 Number theory (11-XX) 22 Algebraic geometry (14-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Dynamical systems and ergodic theory (37-XX)

#### Citations contained in zbMATH

29 Publications have been cited 562 times in 472 Documents Cited by Year
The Brauer-Manin obstruction and $$\text{Ш}[2]$$. Zbl 1222.11084
Bright, M. J.; Bruin, N.; Flynn, E. V.; Logan, A.
2007
Chabauty methods using elliptic curves. Zbl 1135.11320
Bruin, Nils
2003
The Mordell-Weil sieve: proving non-existence of rational points on curves. Zbl 1278.11069
Bruin, Nils; Stoll, Michael
2010
Two-cover descent on hyperelliptic curves. Zbl 1208.11078
Bruin, Nils; Stoll, Michael
2009
Powers from products of consecutive terms in arithmetic progression. Zbl 1178.11033
Bennett, M. A.; Bruin, N.; Győry, K.; Hajdu, L.
2006
Generalized explicit descent and its application to curves of genus 3. Zbl 1408.11065
Bruin, Nils; Poonen, Bjorn; Stoll, Michael
2016
Deciding existence of rational points on curves: an experiment. Zbl 1218.11065
Bruin, Nils; Stoll, Michael
2008
Towers of 2-covers of hyperelliptic curves. Zbl 1145.11317
Bruin, Nils; Flynn, E. Victor
2005
The diophantine equations $$x^2\pm y^4=\pm z^6$$ and $$x^2+y^8=z^3$$. Zbl 0941.11013
Bruin, Nils
1999
On powers as sums of two cubes. Zbl 0986.11021
Bruin, Nils
2000
Some ternary Diophantine equations of signature $$(n,n,2)$$. Zbl 1159.11012
Bruin, Nils
2006
Exhibiting SHA[2] on hyperelliptic Jacobians. Zbl 1118.14035
Bruin, N.; Flynn, E. V.
2006
On finiteness conjectures for endomorphism algebras of abelian surfaces. Zbl 1116.14042
Bruin, Nils; Flynn, E. Victor; Gonzalez, Josep; Rotger, Victor
2006
Trinomials $$ax + bx + c$$ and $$ax + bx+ c$$ with Galois groups of order 168 and $$8\cdot 168$$. Zbl 1058.11044
Bruin, Nils; Elkies, Noam D.
2002
Descent via $$(3,3)$$-isogeny on Jacobians of genus 2 curves. Zbl 1311.11052
Bruin, Nils; Flynn, E. Victor; Testa, Damiano
2014
Minimal models for rational functions in a dynamical setting. Zbl 1300.37051
Bruin, Nils; Molnar, Alexander
2012
Transcendence of generating functions whose coefficients are multiplicative. Zbl 1271.11095
Bell, Jason P.; Bruin, Nils; Coons, Michael
2012
Rational points on twists of $$X_0 (63)$$. Zbl 1158.11027
Bruin, Nils; Fernández, Julio; González, Josep; Lario, Joan-C.
2007
The primitive solutions to $$x^3+y^9=z^2$$. Zbl 1081.11019
Bruin, Nils
2005
The arithmetic of Prym varieties in genus 3. Zbl 1166.11022
Bruin, Nils
2008
Visualising Sha[2] in Abelian surfaces. Zbl 1090.11035
Bruin, Nils
2004
The arithmetic of genus two curves with $$(4,4)$$-split Jacobians. Zbl 1233.11070
Bruin, Nils; Doerksen, Kevin
2011
On congruent primes and class numbers of imaginary quadratic fields. Zbl 1291.11092
Bruin, Nils; Hemenway, Brett
2013
Arithmetic progressions consisting of unlike powers. Zbl 1142.11018
Bruin, N.; Győry, K.; Hajdu, L.; Tengely, Sz.
2006
Rational divisors in rational divisor classes. Zbl 1148.11318
Bruin, N.; Flynn, E. V.
2004
$$N$$-covers of hyperelliptic curves. Zbl 1053.11056
Bruin, N.; Flynn, E. V.
2003
Arithmetic aspects of the Burkhardt quartic threefold. Zbl 1446.11111
Bruin, Nils; Nasserden, Brett
2018
Success and challenges in determining the rational points on curves. Zbl 1344.11048
Bruin, Nils
2013
Visualizing elements of Sha[3] in genus 2 Jacobians. Zbl 1260.11040
Bruin, Nils; Dahmen, Sander R.
2010
Arithmetic aspects of the Burkhardt quartic threefold. Zbl 1446.11111
Bruin, Nils; Nasserden, Brett
2018
Generalized explicit descent and its application to curves of genus 3. Zbl 1408.11065
Bruin, Nils; Poonen, Bjorn; Stoll, Michael
2016
Descent via $$(3,3)$$-isogeny on Jacobians of genus 2 curves. Zbl 1311.11052
Bruin, Nils; Flynn, E. Victor; Testa, Damiano
2014
On congruent primes and class numbers of imaginary quadratic fields. Zbl 1291.11092
Bruin, Nils; Hemenway, Brett
2013
Success and challenges in determining the rational points on curves. Zbl 1344.11048
Bruin, Nils
2013
Minimal models for rational functions in a dynamical setting. Zbl 1300.37051
Bruin, Nils; Molnar, Alexander
2012
Transcendence of generating functions whose coefficients are multiplicative. Zbl 1271.11095
Bell, Jason P.; Bruin, Nils; Coons, Michael
2012
The arithmetic of genus two curves with $$(4,4)$$-split Jacobians. Zbl 1233.11070
Bruin, Nils; Doerksen, Kevin
2011
The Mordell-Weil sieve: proving non-existence of rational points on curves. Zbl 1278.11069
Bruin, Nils; Stoll, Michael
2010
Visualizing elements of Sha[3] in genus 2 Jacobians. Zbl 1260.11040
Bruin, Nils; Dahmen, Sander R.
2010
Two-cover descent on hyperelliptic curves. Zbl 1208.11078
Bruin, Nils; Stoll, Michael
2009
Deciding existence of rational points on curves: an experiment. Zbl 1218.11065
Bruin, Nils; Stoll, Michael
2008
The arithmetic of Prym varieties in genus 3. Zbl 1166.11022
Bruin, Nils
2008
The Brauer-Manin obstruction and $$\text{Ш}[2]$$. Zbl 1222.11084
Bright, M. J.; Bruin, N.; Flynn, E. V.; Logan, A.
2007
Rational points on twists of $$X_0 (63)$$. Zbl 1158.11027
Bruin, Nils; Fernández, Julio; González, Josep; Lario, Joan-C.
2007
Powers from products of consecutive terms in arithmetic progression. Zbl 1178.11033
Bennett, M. A.; Bruin, N.; Győry, K.; Hajdu, L.
2006
Some ternary Diophantine equations of signature $$(n,n,2)$$. Zbl 1159.11012
Bruin, Nils
2006
Exhibiting SHA[2] on hyperelliptic Jacobians. Zbl 1118.14035
Bruin, N.; Flynn, E. V.
2006
On finiteness conjectures for endomorphism algebras of abelian surfaces. Zbl 1116.14042
Bruin, Nils; Flynn, E. Victor; Gonzalez, Josep; Rotger, Victor
2006
Arithmetic progressions consisting of unlike powers. Zbl 1142.11018
Bruin, N.; Győry, K.; Hajdu, L.; Tengely, Sz.
2006
Towers of 2-covers of hyperelliptic curves. Zbl 1145.11317
Bruin, Nils; Flynn, E. Victor
2005
The primitive solutions to $$x^3+y^9=z^2$$. Zbl 1081.11019
Bruin, Nils
2005
Visualising Sha[2] in Abelian surfaces. Zbl 1090.11035
Bruin, Nils
2004
Rational divisors in rational divisor classes. Zbl 1148.11318
Bruin, N.; Flynn, E. V.
2004
Chabauty methods using elliptic curves. Zbl 1135.11320
Bruin, Nils
2003
$$N$$-covers of hyperelliptic curves. Zbl 1053.11056
Bruin, N.; Flynn, E. V.
2003
Trinomials $$ax + bx + c$$ and $$ax + bx+ c$$ with Galois groups of order 168 and $$8\cdot 168$$. Zbl 1058.11044
Bruin, Nils; Elkies, Noam D.
2002
On powers as sums of two cubes. Zbl 0986.11021
Bruin, Nils
2000
The diophantine equations $$x^2\pm y^4=\pm z^6$$ and $$x^2+y^8=z^3$$. Zbl 0941.11013
Bruin, Nils
1999
all top 5

all top 5

#### Cited in 75 Serials

 192 Analysis Mathematica 30 Acta Mathematica Hungarica 23 Journal of Number Theory 16 Transformation Groups 15 Mathematics of Computation 15 International Journal of Number Theory 14 Russian Mathematical Surveys 9 Acta Arithmetica 9 Semigroup Forum 9 Journal de Théorie des Nombres de Bordeaux 8 Vestnik Yuzhno-Ural’skogo Gosudarstvennogo Universiteta. Seriya Matematika. Mekhanika. Fizika 6 Compositio Mathematica 6 Studia Logica 5 Manuscripta Mathematica 5 Applied Mathematics and Mechanics. (English Edition) 5 Acta Mathematicae Applicatae Sinica. English Series 5 Vestnik Yuzhno-Ural’skogo Gosudarstvennogo Universiteta. Seriya Matematicheskoe Modelirovanie i Programmirovanie 4 Journal of Algebra 4 Transactions of the American Mathematical Society 4 Revista Matemática Iberoamericana 4 LMS Journal of Computation and Mathematics 4 Research in Number Theory 3 Periodica Mathematica Hungarica 3 Annales de l’Institut Fourier 3 Duke Mathematical Journal 3 Mathematische Annalen 3 Monatshefte für Mathematik 3 Indagationes Mathematicae. New Series 3 Izvestiya Saratovskogo Universiteta. Novaya Seriya. Seriya Matematika, Mekhanika, Informatika 2 Bulletin of the Australian Mathematical Society 2 Mathematical Proceedings of the Cambridge Philosophical Society 2 Advances in Mathematics 2 Annali di Matematica Pura ed Applicata. Serie Quarta 2 Functiones et Approximatio. Commentarii Mathematici 2 Topology and its Applications 2 Journal of the American Mathematical Society 2 Journal of Algebra and its Applications 2 Forum of Mathematics, Sigma 1 Astrophysics and Space Science 1 Journal of Mathematical Analysis and Applications 1 Rocky Mountain Journal of Mathematics 1 ZAMP. Zeitschrift für angewandte Mathematik und Physik 1 Zhurnal Vychislitel’noĭ Matematiki i Matematicheskoĭ Fiziki 1 Journal of Geometry and Physics 1 Archiv der Mathematik 1 Glasgow Mathematical Journal 1 Journal of Approximation Theory 1 Journal of Geometry 1 Journal of the Mathematical Society of Japan 1 Journal für die Reine und Angewandte Mathematik 1 Mathematische Zeitschrift 1 Mathematika 1 Memoirs of the American Mathematical Society 1 Proceedings of the American Mathematical Society 1 Proceedings of the Edinburgh Mathematical Society. Series II 1 Proceedings of the Japan Academy. Series A 1 Combinatorica 1 Annals of Physics 1 Bulletin of the American Mathematical Society. New Series 1 The New York Journal of Mathematics 1 Bulletin des Sciences Mathématiques 1 Izvestiya: Mathematics 1 The Ramanujan Journal 1 Annals of Mathematics. Second Series 1 Comptes Rendus. Mathématique. Académie des Sciences, Paris 1 Journal of the Institute of Mathematics of Jussieu 1 Advances in Difference Equations 1 BSHM Bulletin 1 Forum of Mathematics, Pi 1 JSIAM Letters 1 Research in the Mathematical Sciences 1 Complex Manifolds 1 Journal of Computational and Engineering Mathematics 1 Proceedings of the American Mathematical Society. Series B 1 Transactions of A. Razmadze Mathematical Institute
all top 5

#### Cited in 55 Fields

 152 Number theory (11-XX) 103 Harmonic analysis on Euclidean spaces (42-XX) 98 Algebraic geometry (14-XX) 68 Approximations and expansions (41-XX) 28 Functions of a complex variable (30-XX) 28 Functional analysis (46-XX) 19 Dynamical systems and ergodic theory (37-XX) 15 Group theory and generalizations (20-XX) 15 Sequences, series, summability (40-XX) 14 Real functions (26-XX) 14 Partial differential equations (35-XX) 13 Ordinary differential equations (34-XX) 13 Operator theory (47-XX) 11 Nonassociative rings and algebras (17-XX) 8 Field theory and polynomials (12-XX) 7 Numerical analysis (65-XX) 6 Mathematical logic and foundations (03-XX) 6 Topological groups, Lie groups (22-XX) 6 Several complex variables and analytic spaces (32-XX) 6 General topology (54-XX) 6 Manifolds and cell complexes (57-XX) 5 Combinatorics (05-XX) 5 Commutative algebra (13-XX) 5 Potential theory (31-XX) 5 Differential geometry (53-XX) 5 Probability theory and stochastic processes (60-XX) 5 Mechanics of deformable solids (74-XX) 4 Associative rings and algebras (16-XX) 4 Mechanics of particles and systems (70-XX) 4 Fluid mechanics (76-XX) 3 General algebraic systems (08-XX) 3 Measure and integration (28-XX) 3 Integral equations (45-XX) 3 Calculus of variations and optimal control; optimization (49-XX) 3 Quantum theory (81-XX) 3 Systems theory; control (93-XX) 3 Information and communication theory, circuits (94-XX) 2 History and biography (01-XX) 2 Linear and multilinear algebra; matrix theory (15-XX) 2 Abstract harmonic analysis (43-XX) 2 Geometry (51-XX) 2 Computer science (68-XX) 2 Operations research, mathematical programming (90-XX) 1 Order, lattices, ordered algebraic structures (06-XX) 1 Category theory; homological algebra (18-XX) 1 Special functions (33-XX) 1 Difference and functional equations (39-XX) 1 Integral transforms, operational calculus (44-XX) 1 Convex and discrete geometry (52-XX) 1 Algebraic topology (55-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Statistics (62-XX) 1 Statistical mechanics, structure of matter (82-XX) 1 Relativity and gravitational theory (83-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX)