Edit Profile (opens in new tab) Ingram, Patrick Co-Author Distance Author ID: ingram.patrick Published as: Ingram, Patrick External Links: MGP Documents Indexed: 46 Publications since 2005, including 8 Additional arXiv Preprints Reviewing Activity: 20 Reviews Co-Authors: 37 Co-Authors with 15 Joint Publications 744 Co-Co-Authors all top 5 Co-Authors 31 single-authored 6 Silverman, Joseph Hillel 4 Jones, Rafe 3 Manes, Michelle 2 Benedetto, Robert L. 2 Everest, Graham Robert 2 Hutz, Benjamin 2 Levy, Alon 2 Mahé, Valéry 2 Stevens, Shaun 2 Tucker, Thomas John 1 Bedford, Eric 1 Bennett, Michael A. 1 Berger, Pierre 1 Bianchi, Fabrizio 1 Bridy, Andrew 1 Buff, Xavier 1 Crovisier, Sylvain 1 Dujardin, Romain 1 Faber, Xander 1 Favre, Charles 1 Firsova, Tanya 1 Fraser, Benjamin A. 1 Ishii, Yutaka 1 Jaramillo-Martinez, David 1 Juul, Jamie 1 Mello, Jorge 1 Palmisano, Liviana 1 Pujals, Enrique Ramiro 1 Raissy, Jasmin 1 Ramadas, Rohini 1 Rubinstein-Salzedo, Simon 1 Stange, Katherine E. 1 Štimac, Sonja 1 Streng, Marco 1 Tien Cuong Dinh 1 Vigny, Gabriel 1 Zieve, Michael E. all top 5 Serials 4 IMRN. International Mathematics Research Notices 3 Canadian Mathematical Bulletin 3 Transactions of the American Mathematical Society 2 Acta Arithmetica 2 Canadian Journal of Mathematics 2 Duke Mathematical Journal 2 Journal of Number Theory 2 Proceedings of the London Mathematical Society. Third Series 2 Mathematical Research Letters 1 Mathematical Proceedings of the Cambridge Philosophical Society 1 Rocky Mountain Journal of Mathematics 1 Bulletin of the London Mathematical Society 1 Journal of the London Mathematical Society. Second Series 1 Journal für die Reine und Angewandte Mathematik 1 Mathematische Zeitschrift 1 Monatshefte für Mathematik 1 Comptes Rendus Mathématiques de l’Académie des Sciences 1 Ergodic Theory and Dynamical Systems 1 Bulletin of the American Mathematical Society. New Series 1 Journal de Théorie des Nombres de Bordeaux 1 LMS Journal of Computation and Mathematics 1 Journal of the Australian Mathematical Society 1 Computational Methods and Function Theory 1 Algebra & Number Theory all top 5 Fields 26 Number theory (11-XX) 24 Dynamical systems and ergodic theory (37-XX) 8 Algebraic geometry (14-XX) 2 Functions of a complex variable (30-XX) 2 Several complex variables and analytic spaces (32-XX) 1 Ordinary differential equations (34-XX) 1 Difference and functional equations (39-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 33 Publications have been cited 236 times in 163 Documents Cited by ▼ Year ▼ Primitive divisors in arithmetic dynamics. Zbl 1242.11012 Ingram, Patrick; Silverman, Joseph H. 30 2009 Current trends and open problems in arithmetic dynamics. Zbl 1468.37001 Benedetto, Robert; Ingram, Patrick; Jones, Rafe; Manes, Michelle; Silverman, Joseph H.; Tucker, Thomas J. 22 2019 Elliptic divisibility sequences over certain curves. Zbl 1170.11010 Ingram, Patrick 15 2007 A finiteness result for post-critically finite polynomials. Zbl 1333.37029 Ingram, Patrick 14 2012 Uniform estimates for primitive divisors in elliptic divisibility sequences. Zbl 1276.11092 Ingram, Patrick; Silverman, Joseph H. 13 2012 On Poonen’s conjecture concerning rational preperiodic points of quadratic maps. Zbl 1316.37042 Hutz, Benjamin; Ingram, Patrick 13 2013 Lower bounds on the canonical height associated to the morphism \(\phi(z)= z^d+c\). Zbl 1239.11071 Ingram, Patrick 12 2009 Attracting cycles in \(p\)-adic dynamics and height bounds for postcritically finite maps. Zbl 1323.37058 Benedetto, Robert; Ingram, Patrick; Jones, Rafe; Levy, Alon 12 2014 Arboreal Galois representations and uniformization of polynomial dynamics. Zbl 1280.37058 Ingram, Patrick 11 2013 Variation of the canonical height for a family of polynomials. Zbl 1297.14028 Ingram, Patrick 9 2013 Finite ramification for preimage fields of post-critically finite morphisms. Zbl 1391.14004 Bridy, Andrew; Ingram, Patrick; Jones, Rafe; Juul, Jamie; Levy, Alon; Manes, Michelle; Rubinstein-Salzedo, Simon; Silverman, Joseph H. 8 2017 Canonical heights for Hénon maps. Zbl 1323.37059 Ingram, Patrick 8 2014 Multiples of integral points on elliptic curves. Zbl 1233.11062 Ingram, Patrick 7 2009 Algebraic divisibility sequences over function fields. Zbl 1251.11008 Ingram, Patrick; Mahé, Valéry; Silverman, Joseph H.; Stange, Katherine E.; Streng, Marco 6 2012 The critical height is a moduli height. Zbl 1395.37068 Ingram, Patrick 6 2018 A quantitative primitive divisor result for points on elliptic curves. Zbl 1208.11073 Ingram, Patrick 5 2009 On \(k\)-th power numerical centres. Zbl 1138.11315 Ingram, Patrick 5 2005 Diophantine analysis and torsion on elliptic curves. Zbl 1117.11033 Ingram, Patrick 4 2007 Uniform bounds on pre-images under quadratic dynamical systems. Zbl 1222.11086 Faber, Xander; Hutz, Benjamin; Ingram, Patrick; Jones, Rafe; Manes, Michelle; Tucker, Thomas J.; Zieve, Michael E. 4 2009 Primitive divisors on twists of Fermat’s cubic. Zbl 1252.11049 Everest, Graham; Ingram, Patrick; Stevens, Shaun 4 2009 Torsion subgroups of elliptic curves in short Weierstrass form. Zbl 1136.11311 Bennett, Michael A.; Ingram, Patrick 4 2005 A lower bound for the canonical height associated to a Drinfeld module. Zbl 1386.11077 Ingram, Patrick 4 2014 The uniform primality conjecture for elliptic curves. Zbl 1246.11117 Everest, Graham; Ingram, Patrick; Mahé, Valéry; Stevens, Shaun 4 2008 Canonical heights for correspondences. Zbl 1410.37094 Ingram, Patrick 3 2019 Rigidity and height bounds for certain post-critically finite endomorphisms of \(\mathbb{P}^N\). Zbl 1391.37077 Ingram, Patrick 3 2016 Critical dynamics of variable-separated affine correspondences. Zbl 1380.37093 Ingram, Patrick 2 2017 Canonical heights and preperiodic points for certain weighted homogeneous families of polynomials. Zbl 1456.37108 Ingram, Patrick 2 2019 \(p\)-adic uniformization and the action of Galois on certain affine correspondences. Zbl 1435.37109 Ingram, Patrick 1 2018 Critical orbits of polynomials with a periodic point of specified multiplier. Zbl 1415.37114 Ingram, Patrick 1 2019 Specializations of elliptic surfaces, and divisibility in the Mordell-Weil group. Zbl 1244.11061 Ingram, Patrick 1 2011 Variation of the canonical height for polynomials in several variables. Zbl 1333.14024 Ingram, Patrick 1 2015 Post-critically finite maps on \(\mathbb{P}^n\) for \(n\ge 2\) are sparse. Zbl 1516.37146 Ingram, Patrick; Ramadas, Rohini; Silverman, Joseph H. 1 2023 Minimally critical regular endomorphisms of \(\mathbb{A}^N\). Zbl 1517.37095 Ingram, Patrick 1 2023 Post-critically finite maps on \(\mathbb{P}^n\) for \(n\ge 2\) are sparse. Zbl 1516.37146 Ingram, Patrick; Ramadas, Rohini; Silverman, Joseph H. 1 2023 Minimally critical regular endomorphisms of \(\mathbb{A}^N\). Zbl 1517.37095 Ingram, Patrick 1 2023 Current trends and open problems in arithmetic dynamics. Zbl 1468.37001 Benedetto, Robert; Ingram, Patrick; Jones, Rafe; Manes, Michelle; Silverman, Joseph H.; Tucker, Thomas J. 22 2019 Canonical heights for correspondences. Zbl 1410.37094 Ingram, Patrick 3 2019 Canonical heights and preperiodic points for certain weighted homogeneous families of polynomials. Zbl 1456.37108 Ingram, Patrick 2 2019 Critical orbits of polynomials with a periodic point of specified multiplier. Zbl 1415.37114 Ingram, Patrick 1 2019 The critical height is a moduli height. Zbl 1395.37068 Ingram, Patrick 6 2018 \(p\)-adic uniformization and the action of Galois on certain affine correspondences. Zbl 1435.37109 Ingram, Patrick 1 2018 Finite ramification for preimage fields of post-critically finite morphisms. Zbl 1391.14004 Bridy, Andrew; Ingram, Patrick; Jones, Rafe; Juul, Jamie; Levy, Alon; Manes, Michelle; Rubinstein-Salzedo, Simon; Silverman, Joseph H. 8 2017 Critical dynamics of variable-separated affine correspondences. Zbl 1380.37093 Ingram, Patrick 2 2017 Rigidity and height bounds for certain post-critically finite endomorphisms of \(\mathbb{P}^N\). Zbl 1391.37077 Ingram, Patrick 3 2016 Variation of the canonical height for polynomials in several variables. Zbl 1333.14024 Ingram, Patrick 1 2015 Attracting cycles in \(p\)-adic dynamics and height bounds for postcritically finite maps. Zbl 1323.37058 Benedetto, Robert; Ingram, Patrick; Jones, Rafe; Levy, Alon 12 2014 Canonical heights for Hénon maps. Zbl 1323.37059 Ingram, Patrick 8 2014 A lower bound for the canonical height associated to a Drinfeld module. Zbl 1386.11077 Ingram, Patrick 4 2014 On Poonen’s conjecture concerning rational preperiodic points of quadratic maps. Zbl 1316.37042 Hutz, Benjamin; Ingram, Patrick 13 2013 Arboreal Galois representations and uniformization of polynomial dynamics. Zbl 1280.37058 Ingram, Patrick 11 2013 Variation of the canonical height for a family of polynomials. Zbl 1297.14028 Ingram, Patrick 9 2013 A finiteness result for post-critically finite polynomials. Zbl 1333.37029 Ingram, Patrick 14 2012 Uniform estimates for primitive divisors in elliptic divisibility sequences. Zbl 1276.11092 Ingram, Patrick; Silverman, Joseph H. 13 2012 Algebraic divisibility sequences over function fields. Zbl 1251.11008 Ingram, Patrick; Mahé, Valéry; Silverman, Joseph H.; Stange, Katherine E.; Streng, Marco 6 2012 Specializations of elliptic surfaces, and divisibility in the Mordell-Weil group. Zbl 1244.11061 Ingram, Patrick 1 2011 Primitive divisors in arithmetic dynamics. Zbl 1242.11012 Ingram, Patrick; Silverman, Joseph H. 30 2009 Lower bounds on the canonical height associated to the morphism \(\phi(z)= z^d+c\). Zbl 1239.11071 Ingram, Patrick 12 2009 Multiples of integral points on elliptic curves. Zbl 1233.11062 Ingram, Patrick 7 2009 A quantitative primitive divisor result for points on elliptic curves. Zbl 1208.11073 Ingram, Patrick 5 2009 Uniform bounds on pre-images under quadratic dynamical systems. Zbl 1222.11086 Faber, Xander; Hutz, Benjamin; Ingram, Patrick; Jones, Rafe; Manes, Michelle; Tucker, Thomas J.; Zieve, Michael E. 4 2009 Primitive divisors on twists of Fermat’s cubic. Zbl 1252.11049 Everest, Graham; Ingram, Patrick; Stevens, Shaun 4 2009 The uniform primality conjecture for elliptic curves. Zbl 1246.11117 Everest, Graham; Ingram, Patrick; Mahé, Valéry; Stevens, Shaun 4 2008 Elliptic divisibility sequences over certain curves. Zbl 1170.11010 Ingram, Patrick 15 2007 Diophantine analysis and torsion on elliptic curves. Zbl 1117.11033 Ingram, Patrick 4 2007 On \(k\)-th power numerical centres. Zbl 1138.11315 Ingram, Patrick 5 2005 Torsion subgroups of elliptic curves in short Weierstrass form. Zbl 1136.11311 Bennett, Michael A.; Ingram, Patrick 4 2005 all cited Publications top 5 cited Publications all top 5 Cited by 174 Authors 15 Ingram, Patrick 12 Hindes, Wade 11 Silverman, Joseph Hillel 9 Tucker, Thomas John 7 Doyle, John R. 7 Ghioca, Dragos 5 Faber, Xander 5 Gauthier, Thomas 5 Hutz, Benjamin 5 Jones, Rafe 5 Ostafe, Alina 4 Benedetto, Robert L. 4 Bridy, Andrew 4 Looper, Nicole R. 4 Manes, Michelle 4 Tornero, José María 4 Vigny, Gabriel 4 Yabuta, Minoru 3 Canci, Jung Kyu 3 González-Jiménez, Enrique 3 Hsia, Liang-Chung 3 Rout, Sudhansu Sekhar 3 Schmidt, Harry 3 Shparlinski, Igor E. 3 Stoll, Michael 3 Streng, Marco 3 Vishkautsan, Solomon 3 Voutier, Paul M. 2 DeMarco, Laura Grace 2 DeMark, David 2 Favre, Charles 2 Ferraguti, Andrea 2 García-Selfa, Irene 2 Granville, Andrew James 2 Lee, Chong Gyu 2 Levy, Alon 2 Li, Ruofan 2 Lukina, Olga 2 Mahé, Valéry 2 Mavraki, Niki Myrto 2 Nguyen, Khoa Dang 2 Petsche, Clayton 2 Reynolds, Jonathan 2 Rumely, Robert S. 2 Stange, Katherine E. 2 Troncoso, Sebastian 2 Verzobio, Matteo 2 Yasufuku, Yu 2 Zhao, Zhengjun 1 Ahmad, Faseeh 1 Akiyama, Shigeki 1 Alfaraj, Abdulmuhsin 1 Allen, Kenneth R. 1 Anderson, Jacqueline 1 Andrews, Jesse 1 Banaszak, Grzegorz 1 Bandeira, Luís 1 Barańczuk, Stefan 1 Bellaïche, Joël 1 Benham, Heidi 1 Bennett, Michael A. 1 Bérczes, Attila 1 Binegar, Skye 1 Bouw, Irene I. 1 Cain, Jennifer 1 Carney, Alexander 1 Carroll, Gregory 1 Carter, Annie 1 Chang, Mei-Chu 1 Chen, Ruqian 1 Chern, Shane 1 Cho, Ilwoo 1 Correia Ramos, Carlos 1 Cortez, Maria Isabel 1 D’Andrea, Carlos 1 Dominick, Randy 1 Dujardin, Romain 1 Ďuriš, Viliam 1 Ejder, Özlem 1 Everest, Graham Robert 1 Faber, X. W. C. 1 Fang, Lily 1 Flatters, Anthony 1 Fujita, Yasutsugu 1 Galarraga, Alexander 1 Galateau, Aurélien 1 Garton, Derek 1 Gassert, Thomas Alden 1 Ghadermarzi, Amir 1 Goksel, Vefa 1 Gomez-Perez, Domingo 1 Gotou, Rin 1 Gregor, Aryeh 1 Gužvić, Tomislav 1 Habegger, Philipp 1 Han, Minsik 1 Huguin, Valentin 1 Hyde, Trevor 1 Jacobs, Kenneth S. 1 Jedrzejak, Tomasz ...and 74 more Authors all top 5 Cited in 67 Serials 20 Journal of Number Theory 13 Transactions of the American Mathematical Society 10 Acta Arithmetica 7 International Journal of Number Theory 6 Journal de Théorie des Nombres de Bordeaux 6 Algebra & Number Theory 5 Proceedings of the American Mathematical Society 5 Ergodic Theory and Dynamical Systems 4 Mathematical Proceedings of the Cambridge Philosophical Society 4 Mathematische Annalen 4 Mathematische Zeitschrift 3 Advances in Mathematics 3 Pacific Journal of Mathematics 3 The New York Journal of Mathematics 2 Rocky Mountain Journal of Mathematics 2 Mathematics of Computation 2 Canadian Mathematical Bulletin 2 Duke Mathematical Journal 2 Journal für die Reine und Angewandte Mathematik 2 IMRN. International Mathematics Research Notices 2 Conformal Geometry and Dynamics 2 LMS Journal of Computation and Mathematics 2 Journal of the European Mathematical Society (JEMS) 2 Integers 2 Comptes Rendus. Mathématique. Académie des Sciences, Paris 2 Involve 2 Research in Number Theory 1 American Mathematical Monthly 1 Israel Journal of Mathematics 1 Periodica Mathematica Hungarica 1 Archiv der Mathematik 1 Bulletin de la Société Mathématique de France 1 Compositio Mathematica 1 Functiones et Approximatio. Commentarii Mathematici 1 Fundamenta Mathematicae 1 Illinois Journal of Mathematics 1 Inventiones Mathematicae 1 Journal of Algebra 1 Journal of the London Mathematical Society. Second Series 1 Journal of Pure and Applied Algebra 1 Manuscripta Mathematica 1 Monatshefte für Mathematik 1 Proceedings of the Japan Academy. Series A 1 Proceedings of the London Mathematical Society. Third Series 1 Revista Matemática Iberoamericana 1 Forum Mathematicum 1 Bulletin of the American Mathematical Society. New Series 1 Indagationes Mathematicae. New Series 1 Experimental Mathematics 1 Finite Fields and their Applications 1 Selecta Mathematica. New Series 1 Opuscula Mathematica 1 Discrete and Continuous Dynamical Systems 1 Journal of the Australian Mathematical Society 1 Journal of Fixed Point Theory and Applications 1 Acta Mathematica Sinica. Chinese Series 1 Journal of Modern Dynamics 1 Asian-European Journal of Mathematics 1 Cryptography and Communications 1 S\(\vec{\text{e}}\)MA Journal 1 Forum of Mathematics, Pi 1 Forum of Mathematics, Sigma 1 Khayyam Journal of Mathematics 1 Arnold Mathematical Journal 1 Journal of Numbers 1 Proceedings of the American Mathematical Society. Series B 1 Annales Henri Lebesgue all top 5 Cited in 18 Fields 121 Number theory (11-XX) 118 Dynamical systems and ergodic theory (37-XX) 41 Algebraic geometry (14-XX) 8 Field theory and polynomials (12-XX) 4 Group theory and generalizations (20-XX) 3 Commutative algebra (13-XX) 3 Functions of a complex variable (30-XX) 3 Several complex variables and analytic spaces (32-XX) 2 Linear and multilinear algebra; matrix theory (15-XX) 2 Topological groups, Lie groups (22-XX) 1 Category theory; homological algebra (18-XX) 1 Real functions (26-XX) 1 Difference and functional equations (39-XX) 1 Functional analysis (46-XX) 1 Operator theory (47-XX) 1 Geometry (51-XX) 1 Differential geometry (53-XX) 1 Probability theory and stochastic processes (60-XX) Citations by Year