## Ingram, Patrick

Compute Distance To:
 Author ID: ingram.patrick Published as: Ingram, Patrick External Links: MGP
 Documents Indexed: 35 Publications since 2005 Reviewing Activity: 20 Reviews Co-Authors: 18 Co-Authors with 11 Joint Publications 369 Co-Co-Authors
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### Co-Authors

 24 single-authored 5 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 Bennett, Michael A. 1 Bridy, Andrew 1 Faber, Xander 1 Juul, Jamie 1 Rubinstein-Salzedo, Simon 1 Stange, Katherine E. 1 Streng, Marco 1 Zieve, Michael E.
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### Serials

 4 IMRN. International Mathematics Research Notices 3 Canadian Mathematical Bulletin 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 Transactions of the American Mathematical Society 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 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 Algebra & Number Theory
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### Fields

 26 Number theory (11-XX) 21 Dynamical systems and ergodic theory (37-XX) 8 Algebraic geometry (14-XX) 1 Functions of a complex variable (30-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Ordinary differential equations (34-XX) 1 Difference and functional equations (39-XX)

### Citations contained in zbMATH Open

30 Publications have been cited 177 times in 122 Documents Cited by Year
Primitive divisors in arithmetic dynamics. Zbl 1242.11012
Ingram, Patrick; Silverman, Joseph H.
2009
Elliptic divisibility sequences over certain curves. Zbl 1170.11010
Ingram, Patrick
2007
On Poonen’s conjecture concerning rational preperiodic points of quadratic maps. Zbl 1316.37042
Hutz, Benjamin; Ingram, Patrick
2013
Uniform estimates for primitive divisors in elliptic divisibility sequences. Zbl 1276.11092
Ingram, Patrick; Silverman, Joseph H.
2012
Lower bounds on the canonical height associated to the morphism $$\phi(z)= z^d+c$$. Zbl 1239.11071
Ingram, Patrick
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.
2019
A finiteness result for post-critically finite polynomials. Zbl 1333.37029
Ingram, Patrick
2012
Attracting cycles in $$p$$-adic dynamics and height bounds for postcritically finite maps. Zbl 1323.37058
Benedetto, Robert; Ingram, Patrick; Jones, Rafe; Levy, Alon
2014
Canonical heights for Hénon maps. Zbl 1323.37059
Ingram, Patrick
2014
Arboreal Galois representations and uniformization of polynomial dynamics. Zbl 1280.37058
Ingram, Patrick
2013
Multiples of integral points on elliptic curves. Zbl 1233.11062
Ingram, Patrick
2009
Algebraic divisibility sequences over function fields. Zbl 1251.11008
Ingram, Patrick; Mahé, Valéry; Silverman, Joseph H.; Stange, Katherine E.; Streng, Marco
2012
Variation of the canonical height for a family of polynomials. Zbl 1297.14028
Ingram, Patrick
2013
On $$k$$-th power numerical centres. Zbl 1138.11315
Ingram, Patrick
2005
A quantitative primitive divisor result for points on elliptic curves. Zbl 1208.11073
Ingram, Patrick
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.
2009
A lower bound for the canonical height associated to a Drinfeld module. Zbl 1386.11077
Ingram, Patrick
2014
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.
2017
Diophantine analysis and torsion on elliptic curves. Zbl 1117.11033
Ingram, Patrick
2007
Torsion subgroups of elliptic curves in short Weierstrass form. Zbl 1136.11311
Bennett, Michael A.; Ingram, Patrick
2005
Primitive divisors on twists of Fermat’s cubic. Zbl 1252.11049
Everest, Graham; Ingram, Patrick; Stevens, Shaun
2009
The uniform primality conjecture for elliptic curves. Zbl 1246.11117
Everest, Graham; Ingram, Patrick; Mahé, Valéry; Stevens, Shaun
2008
The critical height is a moduli height. Zbl 1395.37068
Ingram, Patrick
2018
$$p$$-adic uniformization and the action of Galois on certain affine correspondences. Zbl 1435.37109
Ingram, Patrick
2018
Critical orbits of polynomials with a periodic point of specified multiplier. Zbl 1415.37114
Ingram, Patrick
2019
Canonical heights for correspondences. Zbl 1410.37094
Ingram, Patrick
2019
Specializations of elliptic surfaces, and divisibility in the Mordell-Weil group. Zbl 1244.11061
Ingram, Patrick
2011
Rigidity and height bounds for certain post-critically finite endomorphisms of $$\mathbb{P}^N$$. Zbl 1391.37077
Ingram, Patrick
2016
Variation of the canonical height for polynomials in several variables. Zbl 1333.14024
Ingram, Patrick
2015
Canonical heights and preperiodic points for certain weighted homogeneous families of polynomials. Zbl 1456.37108
Ingram, Patrick
2019
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.
2019
Critical orbits of polynomials with a periodic point of specified multiplier. Zbl 1415.37114
Ingram, Patrick
2019
Canonical heights for correspondences. Zbl 1410.37094
Ingram, Patrick
2019
Canonical heights and preperiodic points for certain weighted homogeneous families of polynomials. Zbl 1456.37108
Ingram, Patrick
2019
The critical height is a moduli height. Zbl 1395.37068
Ingram, Patrick
2018
$$p$$-adic uniformization and the action of Galois on certain affine correspondences. Zbl 1435.37109
Ingram, Patrick
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.
2017
Rigidity and height bounds for certain post-critically finite endomorphisms of $$\mathbb{P}^N$$. Zbl 1391.37077
Ingram, Patrick
2016
Variation of the canonical height for polynomials in several variables. Zbl 1333.14024
Ingram, Patrick
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
2014
Canonical heights for Hénon maps. Zbl 1323.37059
Ingram, Patrick
2014
A lower bound for the canonical height associated to a Drinfeld module. Zbl 1386.11077
Ingram, Patrick
2014
On Poonen’s conjecture concerning rational preperiodic points of quadratic maps. Zbl 1316.37042
Hutz, Benjamin; Ingram, Patrick
2013
Arboreal Galois representations and uniformization of polynomial dynamics. Zbl 1280.37058
Ingram, Patrick
2013
Variation of the canonical height for a family of polynomials. Zbl 1297.14028
Ingram, Patrick
2013
Uniform estimates for primitive divisors in elliptic divisibility sequences. Zbl 1276.11092
Ingram, Patrick; Silverman, Joseph H.
2012
A finiteness result for post-critically finite polynomials. Zbl 1333.37029
Ingram, Patrick
2012
Algebraic divisibility sequences over function fields. Zbl 1251.11008
Ingram, Patrick; Mahé, Valéry; Silverman, Joseph H.; Stange, Katherine E.; Streng, Marco
2012
Specializations of elliptic surfaces, and divisibility in the Mordell-Weil group. Zbl 1244.11061
Ingram, Patrick
2011
Primitive divisors in arithmetic dynamics. Zbl 1242.11012
Ingram, Patrick; Silverman, Joseph H.
2009
Lower bounds on the canonical height associated to the morphism $$\phi(z)= z^d+c$$. Zbl 1239.11071
Ingram, Patrick
2009
Multiples of integral points on elliptic curves. Zbl 1233.11062
Ingram, Patrick
2009
A quantitative primitive divisor result for points on elliptic curves. Zbl 1208.11073
Ingram, Patrick
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.
2009
Primitive divisors on twists of Fermat’s cubic. Zbl 1252.11049
Everest, Graham; Ingram, Patrick; Stevens, Shaun
2009
The uniform primality conjecture for elliptic curves. Zbl 1246.11117
Everest, Graham; Ingram, Patrick; Mahé, Valéry; Stevens, Shaun
2008
Elliptic divisibility sequences over certain curves. Zbl 1170.11010
Ingram, Patrick
2007
Diophantine analysis and torsion on elliptic curves. Zbl 1117.11033
Ingram, Patrick
2007
On $$k$$-th power numerical centres. Zbl 1138.11315
Ingram, Patrick
2005
Torsion subgroups of elliptic curves in short Weierstrass form. Zbl 1136.11311
Bennett, Michael A.; Ingram, Patrick
2005
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### Cited by 134 Authors

 13 Ingram, Patrick 9 Hindes, Wade 8 Silverman, Joseph Hillel 7 Tucker, Thomas John 6 Doyle, John R. 6 Ghioca, Dragos 5 Jones, Rafe 4 Bridy, Andrew 4 Faber, Xander 4 Hutz, Benjamin 4 Looper, Nicole R. 4 Ostafe, Alina 4 Tornero, José María 4 Yabuta, Minoru 3 Benedetto, Robert L. 3 Canci, Jung Kyu 3 Gauthier, Thomas 3 González-Jiménez, Enrique 3 Manes, Michelle 3 Rout, Sudhansu Sekhar 3 Shparlinski, Igor E. 3 Stoll, Michael 3 Vishkautsan, Solomon 3 Voutier, Paul M. 2 DeMark, David 2 Favre, Charles 2 García-Selfa, Irene 2 Granville, Andrew James 2 Hsia, Liang-Chung 2 Lee, Chong Gyu 2 Levy, Alon 2 Mahé, Valéry 2 Nguyen, Khoa Dang 2 Reynolds, Jonathan 2 Rumely, Robert S. 2 Stange, Katherine E. 2 Streng, Marco 2 Troncoso, Sebastian 2 Vigny, Gabriel 2 Yasufuku, Yu 1 Akiyama, Shigeki 1 Allen, Kenneth R. 1 Bandeira, Luís 1 Bennett, Michael A. 1 Bérczes, Attila 1 Binegar, Skye 1 Bouw, Irene I. 1 Carter, Annie 1 Chang, Mei-Chu 1 Chen, Ruqian 1 Chern, Shane 1 Cho, Ilwoo 1 Correia Ramos, Carlos 1 D’Andrea, Carlos 1 DeMarco, Laura Grace 1 Dominick, Randy 1 Dujardin, Romain 1 Ďuriš, Viliam 1 Ejder, Özlem 1 Everest, Graham Robert 1 Faber, X. W. C. 1 Ferraguti, Andrea 1 Flatters, Anthony 1 Fujita, Yasutsugu Fujita 1 Galateau, Aurélien 1 Gassert, Thomas Alden 1 Ghadermarzi, Amir 1 Goksel, Vefa 1 Gomez-Perez, Domingo 1 Gregor, Aryeh 1 Gužvić, Tomislav 1 Han, Minsik 1 Huguin, Valentin 1 Hyde, Trevor 1 Jacobs, Kenneth S. 1 Jedrzejak, Tomasz 1 Ji, Qingzhong 1 Jones, Gareth A. 1 Jørgensen, Palle E. T. 1 Juul, Jamie 1 Kalaycı, Tekgül 1 Karemaker, Valentijn 1 Kenney, Meagan 1 Kovacheva, Yordanka 1 Krieger, Holly 1 Kwon, Hyejin 1 Lalín, Matilde Noemí 1 Levin, Aaron 1 Liptai, Kálmán 1 Luca, Florian 1 Mérai, László 1 Micheli, Giacomo 1 Miller, Alison Beth 1 Misplon, Moses 1 Mocz, Lucia 1 Najman, Filip 1 Nara, Tadahisa 1 Naskrȩcki, Bartosz 1 Okuyama, Yûsuke 1 Olsiewski Healey, Vivian ...and 34 more Authors
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### Cited in 56 Serials

 17 Journal of Number Theory 10 Transactions of the American Mathematical Society 8 Acta Arithmetica 6 International Journal of Number Theory 5 Proceedings of the American Mathematical Society 5 Journal de Théorie des Nombres de Bordeaux 4 Mathematical Proceedings of the Cambridge Philosophical Society 3 Mathematische Zeitschrift 2 Rocky Mountain Journal of Mathematics 2 Mathematics of Computation 2 Canadian Mathematical Bulletin 2 Duke Mathematical Journal 2 Mathematische Annalen 2 Ergodic Theory and Dynamical Systems 2 IMRN. International Mathematics Research Notices 2 The New York Journal of Mathematics 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 Algebra & Number Theory 2 Research in Number Theory 1 American Mathematical Monthly 1 Israel Journal of Mathematics 1 Periodica Mathematica Hungarica 1 Advances in Mathematics 1 Archiv der Mathematik 1 Functiones et Approximatio. Commentarii Mathematici 1 Illinois Journal of Mathematics 1 Inventiones Mathematicae 1 Journal of Algebra 1 Journal of Pure and Applied Algebra 1 Journal für die Reine und Angewandte Mathematik 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 Conformal Geometry and Dynamics 1 Journal of the Australian Mathematical Society 1 Journal of Fixed Point Theory and Applications 1 Journal of Modern Dynamics 1 Involve 1 Asian-European Journal of Mathematics 1 Cryptography and Communications 1 S$$\vec{\text{e}}$$MA Journal 1 Arnold Mathematical Journal 1 Journal of Numbers
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### Cited in 14 Fields

 98 Number theory (11-XX) 80 Dynamical systems and ergodic theory (37-XX) 32 Algebraic geometry (14-XX) 8 Field theory and polynomials (12-XX) 3 Several complex variables and analytic spaces (32-XX) 2 Commutative algebra (13-XX) 2 Linear and multilinear algebra; matrix theory (15-XX) 2 Group theory and generalizations (20-XX) 1 Category theory; homological algebra (18-XX) 1 Real functions (26-XX) 1 Functions of a complex variable (30-XX) 1 Functional analysis (46-XX) 1 Operator theory (47-XX) 1 Probability theory and stochastic processes (60-XX)