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arXiv · 2208.14786

A modular analogue of a problem of Vinogradov

Ratnadeep Acharya·Sary Drappeau·Satadal Ganguly·Olivier Ramaré
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Abstract

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 $I$.

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Ratnadeep Acharya, Sary Drappeau, Satadal Ganguly, Olivier Ramaré. 2022-08-31. A modular analogue of a problem of Vinogradov. https://arxiv.org/abs/2208.14786

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