Rankin--Selberg coefficients in arithmetic progressions modulo prime powers
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866917466983104512 |
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| author | Zhu, Tengyou |
| author_facet | Zhu, Tengyou |
| contents | 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 $\{λ_f(n)^2\}_{n\geq 1}$ have a level of distribution $θ=2/5+3/305-\varepsilon$ in arithmetic progressions $n \equiv a \bmod q$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_05766 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Rankin--Selberg coefficients in arithmetic progressions modulo prime powers Zhu, Tengyou Number Theory 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 $\{λ_f(n)^2\}_{n\geq 1}$ have a level of distribution $θ=2/5+3/305-\varepsilon$ in arithmetic progressions $n \equiv a \bmod q$. |
| title | Rankin--Selberg coefficients in arithmetic progressions modulo prime powers |
| topic | Number Theory |
| url | https://arxiv.org/abs/2605.05766 |