Landau-Siegel zeros and zeros of the derivative of the Riemann zeta function

David W. Farmer; Haseo Ki

doi:10.1016/j.aim.2012.04.020

Landau-Siegel zeros and zeros of the derivative of the Riemann zeta function

David W. Farmer, Haseo Ki

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

4 Citations (Scopus)

Abstract

We show that if the derivative of the Riemann zeta function has sufficiently many zeros close to the critical line, then the zeta function has many closely spaced zeros. This gives a condition on the zeros of the derivative of the zeta function which implies a lower bound of the class numbers of imaginary quadratic fields.

Original language	English
Pages (from-to)	2048-2064
Number of pages	17
Journal	Advances in Mathematics
Volume	230
Issue number	4-6
DOIs	https://doi.org/10.1016/j.aim.2012.04.020
Publication status	Published - 2012 Jul

Bibliographical note

Funding Information:
Haseo Ki was supported by Mid-career Researcher Program through NRF grant funded by the MEST 2010-0008706 .

All Science Journal Classification (ASJC) codes

Mathematics(all)

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10.1016/j.aim.2012.04.020

Cite this

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abstract = "We show that if the derivative of the Riemann zeta function has sufficiently many zeros close to the critical line, then the zeta function has many closely spaced zeros. This gives a condition on the zeros of the derivative of the zeta function which implies a lower bound of the class numbers of imaginary quadratic fields.",

author = "Farmer, {David W.} and Haseo Ki",

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AB - We show that if the derivative of the Riemann zeta function has sufficiently many zeros close to the critical line, then the zeta function has many closely spaced zeros. This gives a condition on the zeros of the derivative of the zeta function which implies a lower bound of the class numbers of imaginary quadratic fields.

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Landau-Siegel zeros and zeros of the derivative of the Riemann zeta function

Abstract

Bibliographical note

All Science Journal Classification (ASJC) codes

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