An Explicit Formula Relating Stieltjes Constants and Li's Numbers

Details An Explicit Formula Relating Stieltjes Constants and Li's Numbers An Explicit Formula Relating Stieltjes Constants and Li's Numbers

2004-06-16

arxiv.org/abs/math/0406312v2

Mathematics

Number Theory

5 pages, 1 figure

Scientific paper

In this paper we present a new formula relating Stieltjes numbers $\gamma
_{n}$ and Laurent coefficinets $\eta_{n}$ of logarithmic derivative of the
Riemann's zeta function. Using it we derive an explicit formula for the
oscillating part of Li's numbers $\overset{\sim}{\lambda}_{n}$ which are
connected with the Riemann hypothesis.

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