Jacob Mayle

activity

20202026

most citedOn the effective version of Serre's open image theorem

3 citations · 3 across the 12 of their papers we have counts for

collaborators

14 papers

math.NT2026

Congruence obstructions in the refined Koblitz conjecture

Sung Min Lee, Jacob Mayle, Rakvi

Let $E / Q$ be an elliptic curve. Zywina's refinement of Koblitz's conjecture predicts that there are infinitely many primes $p$ of good reduction for which $\#E_p(\mathbb{F…

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

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

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.NT2025

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 $ρ_{E, ℓ^{\infty}}$ is surj…

math.NT2024

Opposing Average Congruence Class Biases in the Cyclicity and Koblitz Conjectures for Elliptic Curves

Sung Min Lee, Jacob Mayle, Tian Wang

The cyclicity and Koblitz conjectures ask about the distribution of primes of cyclic and prime-order reduction, respectively, for elliptic curves over $Q$ . In 1976, Serre…

math.NT2023

Computing nonsurjective primes associated to Galois representations of genus $2$ curves

Barinder S. Banwait, Armand Brumer, Hyun Jong Kim +4

For a genus $2$ curve $C$ over $Q$ whose Jacobian $A$ admits only trivial geometric endomorphisms, Serre's open image theorem for abelian surfaces asserts that there are o…

math.NT2022

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…

math.NT2022

Serre curves relative to obstructions modulo 2

Jacob Mayle, Rakvi

We consider elliptic curves $E / Q$ for which the image of the adelic Galois representation $ρ_{E}$ is as large as possible given a constraint on the image modulo 2. For suc…

math.NT2021★ 3 cited

On the effective version of Serre's open image theorem

Jacob Mayle, Tian Wang

Let $E / Q$ be an elliptic curve without complex multiplication. By Serre's open image theorem, the mod $ℓ$ Galois representation $ρ_{E, ℓ}$ of $E$ is surject…

math.NT2020

Curious Squares

Neelima Borade, Jacob Mayle

A curious number is a palindromic number whose base ten representation has the form $a \dots ab \dots ba \dots a$ . In this paper, we determine all curious numbers that are per…

math.NT2020

Rigidity in Elliptic Curve Local-Global Principles

Jacob Mayle

We study the rigidity of the local conditions in two well-known local-global principles for elliptic curves over number fields. In particular, we consider a local-global principle…

math.NT2020

A bound for the image conductor of a principally polarized abelian variety with open Galois image

Jacob Mayle

Let $A$ be a principally polarized abelian variety of dimension $g$ over a number field $K$ . Assume that the image of the adelic Galois representation of $A$ is an open subgroup of…

Congruence obstructions in the refined Koblitz conjecture

Rational Solids with Equal Surface Area and Volume

On the Density of Coprime Reductions of Elliptic Curves

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

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

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

Opposing Average Congruence Class Biases in the Cyclicity and Koblitz Conjectures for Elliptic Curves

Computing nonsurjective primes associated to Galois representations of genus 2 curves

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

Serre curves relative to obstructions modulo 2

On the effective version of Serre's open image theorem

Curious Squares

Rigidity in Elliptic Curve Local-Global Principles

A bound for the image conductor of a principally polarized abelian variety with open Galois image

Computing nonsurjective primes associated to Galois representations of genus $2$ curves