On positive real zeros of theta and L-functions associated with real, even and primitive characters

Stéphane R. Louboutin, Marc Munsch

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Let D range over the positive fundamental discriminants. Let θ(t; xD), t > 0, denote the theta function associated with the real, even and primitive Dirichlet character of conductor D. On the one hand, we prove that there are infinitely many positive discriminants D for which θ(t; xD) has at least one positive real zero. On the other hand, we prove that for a given positive real number t0, there are at least ≥ X= log13=2 X positive fundamental discriminants D ≥X for which θ(t0; xD)= 0.

Original languageEnglish
Pages (from-to)643-665
Number of pages23
JournalPublicationes Mathematicae
Issue number4
Publication statusPublished - 1 Dec 2013
Externally publishedYes


  • Dirichlet characters
  • Mean values.
  • Theta functions

ASJC Scopus subject areas

  • Mathematics(all)

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