A Li-type criterion for zero-free half-planes of Riemann's zeta function

2005/07/18 by Pedro Freitas, Freitas, Pedro
Mathematics · #11M06 #11M26 #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11M06 #msc:11M26

paper · pdf · doi:10.48550/arxiv.math/0507368

15 pages, to appear in the J. London Math. Soc

arxiv created 2005/07/18 · arxiv updated 2009/12/01

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.

Related

• An analytic approach to the Riemann hypothesis
• An investigation of the non-trivial zeros of the Riemann zeta function
• Almost all of the nontrivial zeros of the Riemann zeta-function are on the critical line
• Eigenvalue Density, Li's Positivity, and the Critical Strip
• Expansions of the Riemann Zeta function in the critical strip