Hostname: page-component-8448b6f56d-c47g7 Total loading time: 0 Render date: 2024-04-19T22:17:34.292Z Has data issue: false hasContentIssue false
  • English
  • Français

A LI-TYPE CRITERION FOR ZERO-FREE HALF-PLANES OF RIEMANN'S ZETA FUNCTION

Published online by Cambridge University Press:  24 April 2006

PEDRO FREITAS
PEDRO FREITAS
Affiliation:
Faculdade de Motricidade Humana (TU Lisbon) and Mathematical Physics Group of the University of Lisbon, Complexo Interdisciplinar, Av. Prof. Gama Pinto 2, P-1649-003 Lisboa, Portugalfreitas@cii.fc.ul.pt
Get access

Abstract

We define a sequence of real functions which coincide with Li's coefficients at one and which allow us to extend Li's criterion for the Riemann Hypothesis to yield a necessary and sufficient condition for the existence of zero-free strips inside the critical strip $0<\Re(z)<1$. We study some of the properties of these functions, including their oscillatory behaviour.

Keywords

11M26 (primary)11M06 (secondary)
Type
Notes and Papers
Information
Journal of the London Mathematical Society , Volume 73 , Issue 2 , April 2006 , pp. 399 - 414
Copyright
The London Mathematical Society 2006

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.)