A modular analogue of a problem of Vinogradov

Authors

R. Acharya, Ramakrishna Mission Vivekananda Educational and Research Institute
S. Drappeau, Institut de Mathématiques de Marseille
S. Ganguly, Indian Statistical Institute, Kolkata
O. Ramaré, Institut de Mathématiques de Marseille

Article Type

Research Article

Publication Title

Ramanujan Journal

Abstract

Given a primitive, non-CM, holomorphic cusp form f with normalized Fourier coefficients a(n) and given an interval I⊂ [- 2 , 2] , we study the least prime p such that a(p) ∈ 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.

First Page

365

Last Page

382

DOI

https://doi.org/10.1007/s11139-022-00688-9

Publication Date

10-1-2023

Comments

Open Access, Green

Recommended Citation

Acharya, R.; Drappeau, S.; Ganguly, S.; and Ramaré, O., "A modular analogue of a problem of Vinogradov" (2023). Journal Articles. 3569.
https://digitalcommons.isical.ac.in/journal-articles/3569