A note on the gaps between zeros of Epstein's zeta-functions on the critical line
It is proved that Epstein's zeta-function $ζ_{Q}(s)$, related to a positive definite integral binary quadratic form, has a zero $1/2 + iγ$ with $ T \leq γ\leq T + T^{{3/7} +\varepsilon} $ for sufficiently large positive numbers $T$. This is an improvement of the result by M. Jutila and K. Srinivas (Bull. London Math. Soc. 37 (2005) 45--53).
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