A Li‐Type Criterion for Zero‐Free Half‐Planes of Riemann's Zeta Function | Zendy

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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.

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