J. Voloch

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20242026

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math.NT2026

Rational points on smooth surfaces in $P^{3}$ over finite fields

Yves Aubry, JosÃ© Felipe Voloch

We improve a bound due to the second author on number of rational points on smooth surfaces in $P^{3}$ over finite fields and look at families of surfaces that achieve or ne…

math.NT2026

Doubly isogenous curves of genus two with a rational action of $D_{6}$

Jeremy Booher, Everett W. Howe, Andrew V. Sutherland +1

Let $C$ and $C^{'}$ be curves over a finite field $K$ , provided with embeddings $I^^{1}$ and $Î¹'$ into their Jacobian varieties. Let $D \to C$ and $D^{'} \to C^{'}$ be the pullbacks (via these e…

math.NT2025

The p-adic distance of special points to subvarieties

JosÃ© Felipe Voloch

In a paper of Tate and the author, we conjectured a uniform bound for the p-adic distance of torsion points on a semiabelian variety, not lying in a subvariety, to that subvariety.…

math.NT2025

Ordinary Isogeny Graphs with Level Structure

Derek Perrin, JosÃ© Felipe Voloch

We study $ℓ$ -isogeny graphs of ordinary elliptic curves defined over $F_{q}$ with an added level structure. Given an integer $N$ coprime to $p$ and $ℓ,$ we look at the…

math.NT2024

On the Waring problem with Dickson polynomials modulo a prime

We improve recent results of D. Gomez and A. Winterhof (2010) and of A. Ostafe and I. E. Shparlinski (2011) on the Waring problem with Dickson polynomials in the case of prime fini…

math.NT2024

Factoring polynomials over function fields

Jose Felipe Voloch

If K/k is a function field in one variable of positive characteristic, we describe a general algorithm to factor one-variable polynomials with coefficients in K. The algorithm is f…