Hostname: page-component-cd9895bd7-jn8rn Total loading time: 0 Render date: 2024-12-24T01:53:08.087Z Has data issue: false hasContentIssue false
  • English
  • Français

THE $\unicode[STIX]{x1D703}=\infty$ CONJECTURE IMPLIES THE RIEMANN HYPOTHESIS

Part of: Zeta and $L$-functions: analytic theory

Published online by Cambridge University Press:  26 July 2016

Sandro Bettin  and
Steven M. Gonek
Sandro Bettin
Affiliation:
DIMA - Dipartimento di Matematica, Via Dodecaneso, 35, 16146 Genova, Italy email [email protected]
Steven M. Gonek
Affiliation:
Department of Mathematics, University of Rochester, Rochester, NY 14627, U.S.A. email [email protected]
Get access

Abstract

We show that the $\unicode[STIX]{x1D703}=\infty$ conjecture implies the Riemann hypothesis.

MSC classification

Primary: 11M06: $zeta (s)$ and $L(s, chi)$ 11M26: Nonreal zeros of $zeta (s)$ and $L(s, chi)$; Riemann and other hypotheses
Type
Research Article
Information
Mathematika , Volume 63 , Issue 1 , 2017 , pp. 29 - 33
Copyright
Copyright © University College London 2016 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Conrey, J. B., More than two fifths of the zeros of the Riemann zeta function are on the critical line. J. Reine Angew. Math. 399 1989, 1–26.Google Scholar
Farmer, D. W., Long mollifiers of the Riemann zeta-function. Mathematika 40(1) 1993, 71–87.Google Scholar
Gonek, S. M., Graham, S. W. and Lee, Y., A Generalized Lindelöf Hypothesis, unpublished manuscript.Google Scholar
Levinson, N., More than one third of zeros of Riemann’s zeta-function are on 𝜎 = 1/2. Adv. Math. 13 1974, 383–436.Google Scholar
Pintz, J., Oscillatory properties of M (x) =∑ n⩽x 𝜇(n). I. Acta Arith. 42(1) 1982/1983, 49–55.Google Scholar
Radziwiłł, M., Limitations to mollifying $\unicode[STIX]{x1D701}(s)$ , Preprint 2012, arXiv:math.NT/1207.6583.Google Scholar