A modular analogue of a problem of Vinogradov
Résumé
Given a primitive, non-CM, holomorphic cusp form f with normalized Fourier coefficients a_n and given an interval I, 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.
Domaines
Théorie des nombres [math.NT]
Origine : Fichiers produits par l'(les) auteur(s)