On the exponent of distribution for convolutions of $\mathrm{GL(2)}$ coefficients to smooth moduli
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866910210191261696 |
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| author | Yin, Rongjie |
| author_facet | Yin, Rongjie |
| contents | Let $(λ_f(n))_{n\geqslant1}$ be the Hecke eigenvalues of a holomorphic cusp form $f$. We prove that the exponent of distribution of $λ_f*1$ in arithmetic progressions is as large as $\frac{1}{2}+\frac{1}{46}$ when the modulus $q$ is square-free. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_07945 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the exponent of distribution for convolutions of $\mathrm{GL(2)}$ coefficients to smooth moduli Yin, Rongjie Number Theory 11N37, 11B25, 11N25 Let $(λ_f(n))_{n\geqslant1}$ be the Hecke eigenvalues of a holomorphic cusp form $f$. We prove that the exponent of distribution of $λ_f*1$ in arithmetic progressions is as large as $\frac{1}{2}+\frac{1}{46}$ when the modulus $q$ is square-free. |
| title | On the exponent of distribution for convolutions of $\mathrm{GL(2)}$ coefficients to smooth moduli |
| topic | Number Theory 11N37, 11B25, 11N25 |
| url | https://arxiv.org/abs/2511.07945 |