Small gaps in coefficients of L-functions and B-free numbers in short intervals

Emmanuel Kowalski (1) , Olivier Robert (2) , Jie Wu (3)

1 Laboratoire de mathématiques
2 LA MUSE - Laboratoire de Mathématiques Unifiées de Saint-Etienne
3 IECN - Institut Élie Cartan de Nancy

We discuss questions related to the non-existence of gaps in the series defining modular forms and other arithmetic functions of various types, and improve results of Serre, Balog & Ono and Alkan using new results about exponential sums and the distribution of B-free numbers.

Mots clés: B-free numbers; Fourier coefficients of modular forms; Rankin-Selberg convolution; exponential sums

Domaines: Théorie des nombres [math.NT]

Emmanuel Kowalski, Olivier Robert, Jie Wu. Small gaps in coefficients of L-functions and B-free numbers in short intervals. 2006. ⟨hal-00097121⟩