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

Stéphane R. Louboutin, Marc Munsch

Publikation: Beitrag in einer FachzeitschriftArtikel

Abstract

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.

Originalspracheenglisch
Seiten (von - bis)643-665
Seitenumfang23
FachzeitschriftPublicationes Mathematicae
Jahrgang83
Ausgabenummer4
DOIs
PublikationsstatusVeröffentlicht - 1 Dez 2013
Extern publiziertJa

ASJC Scopus subject areas

  • !!Mathematics(all)

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