A modular analogue of a problem of Vinogradov

Ratnadeep Acharya; Sary Drappeau; Satadal Ganguly; Olivier Ramaré

A modular analogue of a problem of Vinogradov

Number Theory 2022-09-02 v2

Authors: Ratnadeep Acharya , Sary Drappeau , Satadal Ganguly , Olivier Ramaré

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 $I$ .

Keywords

holomorphic cusp form fourier coefficients least prime vinogradov problem modular analogue analytic conductor quadratic non-residue

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@article{arxiv.2208.14786,
  title  = {A modular analogue of a problem of Vinogradov},
  author = {Ratnadeep Acharya and Sary Drappeau and Satadal Ganguly and Olivier Ramaré},
  journal= {arXiv preprint arXiv:2208.14786},
  year   = {2022}
}

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14 pages

A modular analogue of a problem of Vinogradov

Abstract

Keywords

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