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

David W. Farmer, Haseo Ki

Research output: Contribution to journalArticle

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 languageEnglish
Pages (from-to)2048-2064
Number of pages17
JournalAdvances in Mathematics
Volume230
Issue number4-6
DOIs
Publication statusPublished - 2012 Jul 1

Fingerprint

Riemann zeta function
Derivative
Zero
Imaginary Quadratic Field
Class number
Lower bound
Imply
Line

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cite this

@article{529d488df361451f9e9017364bc19b41,
title = "Landau-Siegel zeros and zeros of the derivative of the Riemann zeta function",
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",
year = "2012",
month = "7",
day = "1",
doi = "10.1016/j.aim.2012.04.020",
language = "English",
volume = "230",
pages = "2048--2064",
journal = "Advances in Mathematics",
issn = "0001-8708",
publisher = "Academic Press Inc.",
number = "4-6",

}

Landau-Siegel zeros and zeros of the derivative of the Riemann zeta function. / Farmer, David W.; Ki, Haseo.

In: Advances in Mathematics, Vol. 230, No. 4-6, 01.07.2012, p. 2048-2064.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Landau-Siegel zeros and zeros of the derivative of the Riemann zeta function

AU - Farmer, David W.

AU - Ki, Haseo

PY - 2012/7/1

Y1 - 2012/7/1

N2 - 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.

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.

UR - http://www.scopus.com/inward/record.url?scp=84861173006&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84861173006&partnerID=8YFLogxK

U2 - 10.1016/j.aim.2012.04.020

DO - 10.1016/j.aim.2012.04.020

M3 - Article

AN - SCOPUS:84861173006

VL - 230

SP - 2048

EP - 2064

JO - Advances in Mathematics

JF - Advances in Mathematics

SN - 0001-8708

IS - 4-6

ER -