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.
Originalsprache | englisch |
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Seiten (von - bis) | 643-665 |
Seitenumfang | 23 |
Fachzeitschrift | Publicationes Mathematicae |
Jahrgang | 83 |
Ausgabenummer | 4 |
DOIs | |
Publikationsstatus | Veröffentlicht - 1 Dez. 2013 |
Extern publiziert | Ja |
ASJC Scopus subject areas
- Mathematik (insg.)