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11e45 (primary)

Bulletin of the London Mathematical Society (1)

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GAPS BETWEEN THE ZEROS OF EPSTEIN'S ZETA-FUNCTIONS ON THE CRITICAL LINE
M. JUTILA, K. SRINIVAS
Journal:

Bulletin of the London Mathematical Society / Volume 37 / Issue 1 / January 2005

Published online by Cambridge University Press:

08 February 2005, pp. 45-53

Print publication:

January 2005
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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).