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arXiv · 2605.05766

Rankin--Selberg coefficients in arithmetic progressions modulo prime powers

Tengyou Zhu
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Abstract

Let $\varepsilon>0$ be given. For prime power moduli $q=p^k$ with $k\geq 2$ and $p\neq 3$, and assuming the Ramanujan--Petersson conjecture for $\GL_2$ Maass forms, we prove that the Rankin--Selberg coefficients $\{\lambda_f(n)^2\}_{n\geq 1}$ have a level of distribution $\theta=2/5+3/305-\varepsilon$ in arithmetic progressions $n \equiv a \bmod q$.

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Tengyou Zhu. 2026-05-07. Rankin--Selberg coefficients in arithmetic progressions modulo prime powers. https://arxiv.org/abs/2605.05766

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