J. Silverman

activity

19962023

most citedPrimitive Divisors in Arithmetic Dynamics

49 citations · 273 across the 43 of their papers we have counts for

collaborators

52 papers

math.NT2023

Propagation of Zariski Dense Orbits

Hector Pasten, Joseph H. Silverman

Let $X / K$ be a smooth projective variety defined over a number field, and let $f : X \to X$ be a morphism defined over $K$ . We formulate a number of statements of varying strengths a…

math.NT2023★ 2 cited

The size of semigroup orbits modulo primes

Wade Hindes, Joseph H. Silverman

Let $V$ be a projective variety defined over a number field $K$ , let $S$ be a polarized set of endomorphisms of $V$ all defined over $K$ , and let $P \in V (K)$ . For each prime $\math…

math.NT2022

A Heuristic Subexponential Algorithm to Find Paths in Markoff Graphs Over Finite Fields

Joseph H. Silverman

Charles, Goren, and Lauter [J. Cryptology 22(1), 2009] explained how one can construct hash functions using expander graphs in which it is hard to find paths between specified vert…

math.AG2022

Orbits on K3 Surfaces of Markoff Type

Elena Fuchs, Matthew Litman, Joseph H. Silverman +1

Let $W \subset P^{1} \times P^{1} \times P^{1}$ be a surface given by the vanishing of a $(2, 2, 2)$ -form. These surfaces admit three involutions coming from…

math.NT2021

A Lehmer-type height lower bound for abelian surfaces over function fields

Nicole R. Looper, Joseph H. Silverman

Let $K$ be a 1-dimensional function field over an algebraically closed field of characteristic $0$ , and let $A / K$ be an abelian surface. Under mild assumptions, we prove a Lehmer-t…

math.NT2021

A uniform quantitative Manin-Mumford theorem for curves over function fields

Nicole Looper, Joseph Silverman, Robert Wilms

We prove that any smooth projective geometrically connected non-isotrivial curve of genus $g \geq 2$ over a one-dimensional function field of any characteristic has at most $16g^2+32…