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| Format: | Preprint |
| Published: |
2021
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2110.06855 |
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| _version_ | 1866909063519928320 |
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| author | Kim, Jiseong |
| author_facet | Kim, Jiseong |
| contents | By assuming Vinogradov-Korobov type zero-free regions and the generalized Ramanujan-Petersson conjecture, we establish nontrivial upper bounds for almost all short sums of Fourier coefficients of Hecke-Maass cusp forms for $SL(n,\mathbb{Z})$. As applications, we obtain nontrivial upper bounds for the averages of shifted sums involving coefficients of the Hecke-Maass cusp forms for $SL(n,\mathbb{Z})$. Furthermore, we present a conditional result regarding sign changes of these coefficients. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2110_06855 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Applications of zero-free regions on averages and shifted convolution sums of Hecke eigenvalues Kim, Jiseong Number Theory 11F30, 11N36 By assuming Vinogradov-Korobov type zero-free regions and the generalized Ramanujan-Petersson conjecture, we establish nontrivial upper bounds for almost all short sums of Fourier coefficients of Hecke-Maass cusp forms for $SL(n,\mathbb{Z})$. As applications, we obtain nontrivial upper bounds for the averages of shifted sums involving coefficients of the Hecke-Maass cusp forms for $SL(n,\mathbb{Z})$. Furthermore, we present a conditional result regarding sign changes of these coefficients. |
| title | Applications of zero-free regions on averages and shifted convolution sums of Hecke eigenvalues |
| topic | Number Theory 11F30, 11N36 |
| url | https://arxiv.org/abs/2110.06855 |