J. Rouse

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20242026

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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…