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A Li‐Type Criterion for Zero‐Free Half‐Planes of Riemann's Zeta Function
Author(s) -
Freitas Pedro
Publication year - 2006
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/s0024610706022599
Subject(s) - zero (linguistics) , mathematics , riemann hypothesis , mathematical analysis , riemann zeta function , type (biology) , sequence (biology) , function (biology) , yield (engineering) , pure mathematics , physics , chemistry , thermodynamics , ecology , biochemistry , evolutionary biology , biology , philosophy , linguistics
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 < R( z ) < 1. We study some of the properties of these functions, including their oscillatory behaviour.