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GAPS BETWEEN THE ZEROS OF EPSTEIN'S ZETA-FUNCTIONS ON THE CRITICAL LINE

Published online by Cambridge University Press:  08 February 2005

M. JUTILA  and
K. SRINIVAS
M. JUTILA
Affiliation:
Department of Mathematics, University of Turku, FIN-20014 Turku, Finlandjutila@utu.fi
K. SRINIVAS
Affiliation:
Institute of Mathematical Sciences, Tharamani P. O., Chennai-600113, Indiasrini@imsc.res.in
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Abstract

It is proved that Epstein's zeta-function $\zeta_Q(s)$, related to a positive definite integral binary quadratic form, has a zero $ 1/2 +i\gamma $ with $T \leq \gamma \leq T+T^{5/11+\varepsilon }$ for sufficiently large positive numbers $T$. This improves a classical result of H. S. A. Potter and E. C. Titchmarsh (Proc. London Math. Soc. (2) 39 (1935) 372–384).

Keywords

11E45 (primary)11M41 (secondary)
Type
Papers
Information
Bulletin of the London Mathematical Society , Volume 37 , Issue 1 , January 2005 , pp. 45 - 53
Copyright
© The London Mathematical Society 2005

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