JournalsrmiVol. 23, No. 1pp. 281–326

Small gaps in coefficients of LL-functions and B\mathfrak{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\mathfrak{B}-free numbers.

Cite this article

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

DOI 10.4171/RMI/496