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
- Effective finiteness of solutions to certain differential and difference equations draft available on the
- Degree gaps for multipliers and the dynamical Andre-Oort conjecture , to appear. Draft available on the
- Minimally critical regular endomorphisms of \mathbb{A} ^ \Nu Draft available on the
- Minimally critical endomorphisms of \mathbb{P}^\Nu Draft available on the
- Post-Critically Finite Maps on \mathbb{P}^n for n \geq 2 are Sparsewith and Draft available on the
- Current Trends and Open Problems in Arithmetic Dynamics with , , , , , and , Volume 56, Number 4, October 2019, Pages 611–685, , Published: 12 January 2018. Draft available on the
- Critical orbits of polynomials with a periodic point of specified multiplier. Draft available on the , 291, pp. 1245–1262 (2019)
- The critical height is a moduli height. Draft available on the , Volume 167, Number 7 (2018), pp. 1311-1346.
- p-adic uniformization and the action of Galois on certain affine correspondences.Draft available on the , Volume 61 (2018), pp. 531-542
- Canonical heights and pre-periodic points for weighted homogeneous families of polynomials. Draft available on the , , Published: 12 January 2018
- Finite ramification for preimage fields of postcritically finite morphisms with , , , , , , and . Draft available on the , Volume 24 (2017), Number 6
- Critical dynamics of variable-separated affine correspondences. Draft available on the , Volume 95, Issue 3, June 2017, pp. 1011-1034
- Canonical heights for correspondences. Draft available on the Trans. Amer. Math. Soc., DOI: , Published electronically: May 30, 2018
- Rigidity and height bounds for certain post-critically finite endomorphisms of projective space. Draft available on the , Volume 68 (2016), pp. 625-654
- The torsion submodule of an abelian t-module in preparation
- Variation of the canonical height for polynomials in several variables. Draft available on the , Vol. 2015, No. 24, pp. 13545-13562
- The filled Julia set of a Drinfeld module and uniform bounds for torsion submitted,
- A lower bound for the canonical height associated to a Drinfeld module , to appear. Draft available on the
- Attracting cycles in p-adic dynamics and height bounds for post-critically finite maps with , , and , Volume 163, Number 13 (2014), pp. 2325-2356. Draft available on the
- Canonical heights for Hénon maps , Volume 108 (2014), no. 3, pp. 780-808. Draft available on the
- Algebraic divisibility sequences over function fields with , , , 92 (2012), pp. 99-126. Draft available on the
- Arboreal Galois representations and uniformization of polynomial dynamics , Volume 45 (2013), no. 2, pp. 301-308. Draft available on the
- A finiteness result for post-critically finite polynomials , issue 3 (2012), pp. 524-543. Draft available on the
- Variation of the canonical height for a family of polynomials , Volume 685 (2013), pp. 73-97. Draft available on the
- Cubic polynomials with periodic cycles of a specified multiplier , 64 no. 2 (2012), pp. 318-345. Draft available on the
- Specializations of elliptic surfaces, and divisibility in the Mordell-Weil group , 5 no. 4 (2011), pp. 465-493. Draft available on the
- On Poonen's conjecture concerning rational pre-periodic points of quadratic maps with , Volume 43, Number 1 (2013), pp. 193-204. Draft available on the
- Uniform bounds on pre-images under quadratic dynamical systems with , , , , , and 16 number 1 (2009), pp. 87-101. Draft available on the
- A quantitative primitive divisor result for elliptic divisibility sequences , 21 fascicule 3 (2009), pp. 609-634
- Primitive divisors on twists of the Fermat cubicwith G. Everest and , 12 (2009), pp. 54-81. Draft available on the
- Multiples of integral points on elliptic curves , 129 issue 1 (2009), pp. 182-208. Draft available on the
- The uniform primality conjecture for elliptic curves with G. Everest, , and Acta Arithmetica, 134 (2008), pp. 157-181. Draft available on the
- Lower bounds on the canonical height associated to the morphism \phi(z)= z^d + c , 157 (2009), pp. 69-89. Draft available on the
- Primitive divisors in arithmetic dynamics with , 146 issue 2 (2009), pp. 289-302. Draft available on the
- Uniform estimates for primitive divisors in elliptic divisibility sequences with 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 ,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 , 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 357 no. 8 (2005), pp. 3325-3337