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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
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).
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- © The London Mathematical Society 2005
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