A modular analogue of a problem of Vinogradov
| Autor: | Acharya, Ratnadeep, Drappeau, Sary, Ganguly, Satadal, Ramaré, Olivier |
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| Rok vydání: | 2022 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | Given a primitive, non-CM, holomorphic cusp form $f$ with normalized Fourier coefficients $a(n)$ and given an interval $I\subset [-2, 2]$, we study the least prime $p$ such that $a(p)\in I$ . This can be viewed as a modular form analogue of Vinogradov's problem on the least quadratic non-residue. We obtain strong explicit bounds on $p$, depending on the analytic conductor of $f$ for some specific choices of $I$. Comment: 14 pages |
| Databáze: | arXiv |
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