The Néron Fiber of Abelian Varieties with Potential Good Reduction.
Arithmetic Distance Functions and Height Fuctions in Diophantine Geometry.
Rational points on K3 surfaces: A new canonical height.
Integral points on abelian surfaces are widely spaced
The field of definition for dynamical systems on
Geometric and arithmetic properties of the Hénon map.
Heights and the specialization map for families of abelian varieties.
Variation of the canonical height on elliptic surfaces I: Three examples.
A quantitative version of Siegel's theorem: integral points on elliptic curves and Catalan curves.
Integral points on Abelian varieties.
Elliptic Carmichael numbers and elliptic Korselt criteria
Lehmer’s conjecture for polynomials satisfying a congruence divisibility condition and an analogue for elliptic curves
A number of authors have proven explicit versions of Lehmer’s conjecture for polynomials whose coefficients are all congruent to modulo . We prove a similar result for polynomials that are divisible in by a polynomial of the form for some . We also formulate and prove an analogous statement for elliptic curves.
Periodic points, multiplicities, and dynamical units.
The number of elliptic curves over Q with conductor N.
Canonical heights on varieties with morphisms
Terms in elliptic divisibility sequences divisible by their indices
A local-global criterion for dynamics on ℙ¹
Variation of periods modulo in arithmetic dynamics.
Exceptional units and numbers of small Mahler measure.
Divisibility sequences and powers of algebraic integers.
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