Effective method of computing Li's coefficients and their properties

2004/02/11 by Maslanka, Krzysztof
#11M26 #FOS: Mathematics #Number Theory (math.NT) #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.math/0402168

Abstract

In this paper we present an effective method for computing certain real coefficients λ_n which appear in a criterion for the Riemann hypothesis proved by Xian-Jin Li. With the use of this method a sequence of over three-thousand λ_n's has been calculated. This sequence reveals a peculiar and unexpected behavior: it can be split into a strictly growing trend and some tiny oscillations superimposed on this trend.

Related

• A sharpening of Li's criterion for the Riemann Hypothesis
• Some possible approaches to the Riemann Hypothesis via the Li/Keiper constants
• Recurrence relations of Li coefficients
• Simplifications of the Keiper/Li approach to the Riemann Hypothesis
• Densities, Laplace Transforms and Analytic Number Theory