Open Access
April, 2007 Small gaps in coefficients of $L$-functions and $\mathfrak{B}$-free numbers in short intervals
Emmanuel Kowalski, Olivier Robert, Jie Wu
Rev. Mat. Iberoamericana 23(1): 281-326 (April, 2007).


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 $\mathfrak{B}$-free numbers.


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Emmanuel Kowalski. Olivier Robert. Jie Wu. "Small gaps in coefficients of $L$-functions and $\mathfrak{B}$-free numbers in short intervals." Rev. Mat. Iberoamericana 23 (1) 281 - 326, April, 2007.


Published: April, 2007
First available in Project Euclid: 1 June 2007

zbMATH: 1246.11099
MathSciNet: MR2351136

Primary: 11F12 , 11F30 , 11F66 , 11L15 , 11N25

Keywords: $\mathfrak{B}$-free numbers , exponential sums , Fourier coefficients of modular forms , Rankin-Selberg convolution

Rights: Copyright © 2007 Departamento de Matemáticas, Universidad Autónoma de Madrid

Vol.23 • No. 1 • April, 2007
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