These are listed in approximate reverse chronological order. Please note that draft versions on the arXiv may differ from published versions, and only the journal versions are "official."
- Solutions to difference equations have few defectsdraft available on the arxiv
- Effective finiteness of solutions to certain differential and difference equations draft available on the arxiv
- Degree gaps for multipliers and the dynamical Andre-Oort conjecture Canadian Math. Bulletin, to appear. Draft available on the arxiv
- Minimally critical regular endomorphisms of \mathbb{A} ^ \Nu Draft available on the arxiv
- Minimally critical endomorphisms of \mathbb{P}^\Nu Draft available on the arxiv
- Post-Critically Finite Maps on \mathbb{P}^n for n \geq 2 are Sparsewith Rohini Ramadas and Joseph H. Silverman Draft available on the arxiv
- Current Trends and Open Problems in Arithmetic Dynamics with Rob Benedetto, Laura DeMarco, Rafe Jones, Michelle Manes, Joseph H. Silverman, and Thomas J. TuckerBulletin (New Series) of the AMS, Volume 56, Number 4, October 2019, Pages 611–685, https://doi.org/10.1090/bull/1665, Published: 12 January 2018. Draft available on the arxiv
- Critical orbits of polynomials with a periodic point of specified multiplier. Draft available on the arxivMath. Zeitschrift, 291, pp. 1245–1262 (2019)
- The critical height is a moduli height. Draft available on the arXiv Duke Math. J., Volume 167, Number 7 (2018), pp. 1311-1346.
- p-adic uniformization and the action of Galois on certain affine correspondences.Draft available on the arXivCanadian Math. Bull., https://doi.org/10.4153/CMB-2017-082-7 Volume 61 (2018), pp. 531-542
- Canonical heights and pre-periodic points for weighted homogeneous families of polynomials. Draft available on the arXivInt. Math. Res. Not., https://doi.org/10.1093/imrn/rnx291, Published: 12 January 2018
- Finite ramification for preimage fields of postcritically finite morphisms with Andrew Bridy, Rafe Jones, Jamie Juul, Alon Levy, Michelle Manes, Simon Rubinstein-Salzedo, and Joseph H. Silverman. Draft available on the arXivMath. Research Letters, Volume 24 (2017), Number 6
- Critical dynamics of variable-separated affine correspondences. Draft available on the arXivJ. London Math. Soc., Volume 95, Issue 3, June 2017, pp. 1011-1034
- Canonical heights for correspondences. Draft available on the arXivTrans. Amer. Math. Soc., DOI: https://doi.org/10.1090/tran/7288, Published electronically: May 30, 2018
- Rigidity and height bounds for certain post-critically finite endomorphisms of projective space. Draft available on the arXivCanadian Journal of Mathematics, Volume 68 (2016), pp. 625-654 (see also!)
- The torsion submodule of an abelian t-module in preparation
- Variation of the canonical height for polynomials in several variables. Draft available on the arXiv International Mathematics Research Notices, Vol. 2015, No. 24, pp. 13545-13562
- The filled Julia set of a Drinfeld module and uniform bounds for torsion submitted, arXiv
- A lower bound for the canonical height associated to a Drinfeld module International Mathematics Research Notices, to appear. Draft available on the arXiv
- Attracting cycles in p-adic dynamics and height bounds for post-critically finite maps with Rob Benedetto, Rafe Jones, and Alon LevyDuke Mathematical Journal, Volume 163, Number 13 (2014), pp. 2325-2356. Draft available on the arXiv
- Canonical heights for Hénon maps Proceedings of the London Mathematical Society, Volume 108 (2014), no. 3, pp. 780-808. Draft available on the arXiv
- Algebraic divisibility sequences over function fields with V. Mahé, J. H. Silverman, K. E. Stange, M. StrengJournal of the Australian Mathematical Society 92 (2012), pp. 99-126. Draft available on the arXiv
- Arboreal Galois representations and uniformization of polynomial dynamics Bulletin of the London Mathematical Society, Volume 45 (2013), no. 2, pp. 301-308. Draft available on the arXiv
- A finiteness result for post-critically finite polynomials International Mathematics Research Notices, issue 3 (2012), pp. 524-543. Draft available on the arXiv
- Variation of the canonical height for a family of polynomials Journal fur die reine und angewandte Mathematik, Volume 685 (2013), pp. 73-97. Draft available on the arXiv
- Cubic polynomials with periodic cycles of a specified multiplier Canadian Journal of Mathematics, 64 no. 2 (2012), pp. 318-345. Draft available on the arXiv
- Specializations of elliptic surfaces, and divisibility in the Mordell-Weil group Algebra and Number Theory , 5 no. 4 (2011), pp. 465-493. Draft available on the arXiv
- On Poonen's conjecture concerning rational pre-periodic points of quadratic maps with B. HutzRocky Mountain Journal of Mathematics, Volume 43, Number 1 (2013), pp. 193-204. Draft available on the arXiv
- Uniform bounds on pre-images under quadratic dynamical systems with X. W. C. Faber, B. Hutz, R. Jones, M. Manes, T. J. Tucker, and M. E. ZieveMathematical Research Letters 16 number 1 (2009), pp. 87-101. Draft available on the arXiv
- A quantitative primitive divisor result for elliptic divisibility sequences Journal de Théorie des Nombres de Bordeaux, 21 fascicule 3 (2009), pp. 609-634
- Primitive divisors on twists of the Fermat cubicwith G. Everest and S. StevensLMS Journal of Computation and Mathematics, 12 (2009), pp. 54-81. Draft available on the arXiv
- Multiples of integral points on elliptic curves Journal of Number Theory, 129 issue 1 (2009), pp. 182-208. Draft available on the arXiv
- The uniform primality conjecture for elliptic curves with G. Everest, V. Mahé, and S. Stevens Acta Arithmetica, 134 (2008), pp. 157-181. Draft available on the arXiv
- Lower bounds on the canonical height associated to the morphism \phi(z)= z^d + c Monatshefte für Mathematik, 157 (2009), pp. 69-89. Draft available on the arXiv
- Primitive divisors in arithmetic dynamics with J. H. SilvermanMathematical Proceedings of the Cambridge Philosophical Society, 146 issue 2 (2009), pp. 289-302. Draft available on the arXiv
- Uniform estimates for primitive divisors in elliptic divisibility sequences with J. H. SilvermanNumber Theory, Analysis and Geometry Springer-Verlag, 2012
- Approximating algebraic numbers by j-invariants of elliptic curves Acta Arithmetica, 131 (2008), pp. 57-68. Draft available
- Elliptic divisibility sequences over certain curves Journal of Number Theory ,123 issue 2 (2007), pp. 473-486. Received one of twenty "Top Cited Article 2007 - 2011" awards from JNTa draft, fraught with errors, is available
- Diophantine analysis and torsion on elliptic curves Proceedings of the London Mathematical Society, 94 no. 1 (2007), pp. 137-154.
- On k-th power numerical centres Comptes rendus mathematiques de l'Academie des sciences (2006) a draft is available
- Torsion subgroups of elliptic curves in short Weierstrass form with M. A. BennettTransactions of the American Mathematical Society 357 no. 8 (2005), pp. 3325-3337