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ON SIMPLE ZEROS OF THE DEDEKIND ZETA‐FUNCTION OF A QUADRATIC NUMBER FIELD
Author(s) -
Wu Xiaosheng,
Zhao Lilu
Publication year - 2019
Publication title -
mathematika
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.955
H-Index - 29
eISSN - 2041-7942
pISSN - 0025-5793
DOI - 10.1112/s0025579319000196
Subject(s) - mathematics , dedekind cut , rectangle , algebraic number field , simple (philosophy) , function field , riemann zeta function , arithmetic zeta function , prime zeta function , field (mathematics) , function (biology) , quadratic equation , combinatorics , pure mathematics , geometry , philosophy , epistemology , evolutionary biology , biology
We study the number of non‐trivial simple zeros of the Dedekind zeta‐function of a quadratic number field in the rectangle { + i t : 0 < < 1 , 0 < t < T } . We prove that such a number exceeds T 6 / 7 − if T is sufficiently large. This improves upon the classical lower bound T 6 / 11established by Conrey et al [Simple zeros of the zeta function of a quadratic number field. I. Invent. Math. 86 (1986), 563–576].
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