Effective method of computing Li's coefficients and their properties

Abstract

In this paper we present an effective method for computing certain real coefficients ${\lambda }_n$ 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 ${\lambda }_n$'s has been calculated. This sequence reveals a peculiar and unexpected behavior: it can be split into a strictly growing \textit{trend} and some tiny \textit{oscillations} superimposed on this trend.

11 pages, 7 figures

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