J. Rouse

activity

20242026

collaborators

5 papers

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

Modular Forms with Only Nonnegative Coefficients

Paul Jenkins, Jeremy Rouse

We study modular forms for $SL_{2} (Z)$ with no negative Fourier coefficients. Let $A (k)$ be the positive integer where if the first $A (k)$ Fourier coefficients of a…

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

Near coincidences and nilpotent division fields

Harris Daniels, Jeremy Rouse

Let $E / Q$ be an elliptic curve. We say that $E$ has a near coincidence of level $(n, m)$ if $m ∣ n$ and $Q (E [n]) = Q (E [m], ζ_{n})$ . We classify near coi…