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Gaps Between the Zeros of Epstein's Zeta‐Functions on the Critical Line
Author(s) -
Jutila M.,
Srinivas K.
Publication year - 2005
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/s0024609304003716
Subject(s) - mathematics , critical line , zero (linguistics) , mathematics subject classification , line (geometry) , quadratic equation , riemann zeta function , function (biology) , pure mathematics , combinatorics , geometry , condensed matter physics , physics , philosophy , linguistics , evolutionary biology , biology
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+ i γ with T ⩽ γ ⩽ T + T 5/11+ɛ 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). 2000 Mathematics Subject Classification 11E45 (primary), 11M41 (secondary).