Gaps between zeros of the Riemann zeta-function

H. M. Bui; M. B. Milinovich

doi:10.1093/qmath/hax047

Gaps between zeros of the Riemann zeta-function

H. M. Bui, M. B. Milinovich

University of Mississippi

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

281 Downloads (Pure)

Abstract

We prove that there exist infinitely many consecutive zeros of the Riemann zeta-function on the critical line whose gaps are greater than 3.18 times the average spacing. Using a modification of our method, we also show that there are even larger gaps between the multiple zeros of the Riemann zeta-function on the critical line (if such zeros exist).

Original language	English
Pages (from-to)	403-423
Number of pages	21
Journal	Quarterly Journal of Mathematics
Volume	69
Issue number	2
Early online date	26 Sept 2017
DOIs	https://doi.org/10.1093/qmath/hax047
Publication status	Published - Jun 2018

Access to Document

10.1093/qmath/hax047

QJM submittedAccepted author manuscript, 337 KB

Cite this

@article{32f57b4d8a3f4b8b8f1b9ceceb29781b,

title = "Gaps between zeros of the Riemann zeta-function",

abstract = "We prove that there exist infinitely many consecutive zeros of the Riemann zeta-function on the critical line whose gaps are greater than 3.18 times the average spacing. Using a modification of our method, we also show that there are even larger gaps between the multiple zeros of the Riemann zeta-function on the critical line (if such zeros exist).",

author = "Bui, {H. M.} and Milinovich, {M. B.}",

year = "2018",

month = jun,

doi = "10.1093/qmath/hax047",

language = "English",

volume = "69",

pages = "403--423",

journal = "Quarterly Journal of Mathematics",

issn = "0033-5606",

publisher = "Oxford University Press",

number = "2",

}

TY - JOUR

T1 - Gaps between zeros of the Riemann zeta-function

AU - Bui, H. M.

AU - Milinovich, M. B.

PY - 2018/6

Y1 - 2018/6

N2 - We prove that there exist infinitely many consecutive zeros of the Riemann zeta-function on the critical line whose gaps are greater than 3.18 times the average spacing. Using a modification of our method, we also show that there are even larger gaps between the multiple zeros of the Riemann zeta-function on the critical line (if such zeros exist).

AB - We prove that there exist infinitely many consecutive zeros of the Riemann zeta-function on the critical line whose gaps are greater than 3.18 times the average spacing. Using a modification of our method, we also show that there are even larger gaps between the multiple zeros of the Riemann zeta-function on the critical line (if such zeros exist).

UR - http://www.scopus.com/inward/record.url?scp=85044878737&partnerID=8YFLogxK

U2 - 10.1093/qmath/hax047

DO - 10.1093/qmath/hax047

M3 - Article

SN - 0033-5606

VL - 69

SP - 403

EP - 423

JO - Quarterly Journal of Mathematics

JF - Quarterly Journal of Mathematics

IS - 2

ER -

Gaps between zeros of the Riemann zeta-function

Abstract

Access to Document

Other files and links

Fingerprint

Cite this