Effective method of computing Li's coefficients and their properties

Details Effective method of computing Li's coefficients and their properties Effective method of computing Li's coefficients and their properties

2004-02-11

arxiv.org/abs/math/0402168v5

Mathematics

Number Theory

11 pages, 7 figures

Scientific paper

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.

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