An Explicit Formula Relating Stieltjes Constants and Li's Numbers

Abstract

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 ${\stackrel{\sim }{\lambda }}_n$ which are connected with the Riemann hypothesis.

5 pages, 1 figure

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