Back to Search Start Over

A modular analogue of a problem of Vinogradov

Authors :
Acharya, Ratnadeep
Drappeau, Sary
Ganguly, Satadal
Ramaré, Olivier
Publication Year :
2022

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 $I$.<br />Comment: 14 pages

Details

Database :
arXiv
Publication Type :
Report
Accession number :
edsarx.2208.14786
Document Type :
Working Paper