Institut de Mathématiques de Luminy

Abstract 2004-16

Jutila Matti, Srinivas Kotyada.
Gaps between the zeros of Epstein's zeta-functions on the critical line.

It is proved that Epstein’s zeta-function ζQ(s) related to a positive definite integral binary quadratic form has a zero 1/2 + iγ with T ≤ γ ≤ T + T5/11+ε for sufficiently large positive numbers T. This improves a classical result of H. S. A. Potter and E. C. Titchmarsh.


Last update : november 2, 2004, EL.