Small gaps in coefficients of $L$-functions and $\mathfrak{B}$-free numbers in short intervals

Emmanuel Kowalski; Olivier Robert; Jie Wu

doi:10.4171/rmi/496

JournalsrmiVol. 23, No. 1pp. 281–326

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

Emmanuel Kowalski
Université de Bordeaux I, Talence, France
Olivier Robert
Université Jean-Monnet, Saint-Etienne, France
Jie Wu
Université Henri Poincaré, Vandoeuvre lès Nancy, France

$Small gaps in coefficients of $L$-functions and $\mathfrak{B}$-free numbers in short intervals cover$

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Abstract

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 and Ono, and Alkan using new results about exponential sums and the distribution of $B$ -free numbers.

Cite this article

Emmanuel Kowalski, Olivier Robert, Jie Wu, Small gaps in coefficients of $L$ -functions and $B$ -free numbers in short intervals. Rev. Mat. Iberoam. 23 (2007), no. 1, pp. 281–326

DOI 10.4171/RMI/496