Jacob Mayle

activity

20242026

collaborators

6 papers

math.NT2026

Rational Solids with Equal Surface Area and Volume

Kate Finnerty, Jacob Mayle

We classify pairs consisting of a right square pyramid and a right square prism, each having rational base side length and rational height, for which the two solids have equal surf…

math.NT2026

Rational points on modular curves via maps to elliptic curves with rank zero

Jacob Mayle, Jeremy Rouse

A fundamental problem in arithmetic geometry is to determine the image of the mod $N$ Galois representation for all elliptic curves over $Q$ and integers $N \geq 1$ . For a…

math.NT2026

On the Density of Coprime Reductions of Elliptic Curves

Asimina S. Hamakiotes, Sung Min Lee, Jacob Mayle +1

Given non-CM elliptic curves $E_{1}$ and $E_{2}$ over $Q$ , we study the natural density of primes $p$ of good reduction for which the orders of the groups $E_{1} (F_{p})$ …

math.NT2026

The possible adelic indices for elliptic curves admitting a rational cyclic isogeny

Kate Finnerty, Tyler Genao, Jacob Mayle +1

In the 1970s, Serre proved that the adelic index of a non-CM elliptic curve over a number field is finite. More recently, Zywina conjectured the complete set of adelic indices for…

math.NT2025

A uniform bound on the smallest surjective prime of an elliptic curve

Tyler Genao, Jacob Mayle, Jeremy Rouse

Let $E / Q$ be an elliptic curve without complex multiplication. A well-known theorem of Serre asserts that the $ℓ$ -adic Galois representation $I ¨ _{E, ℓ^{\infty}}$ is sur…

math.NT2024

An effective open image theorem for products of principally polarized abelian varieties

Jacob Mayle, Tian Wang

Let $A = \prod_{1 \leq i \leq n} A_{i}$ be the product of principally polarized abelian varieties $A_{1}, \dots, A_{n}$ of dimensions $g_{1}, \dots, g_{n}$ , respectively, each defined over a…