An Explicit Formula Relating Stieltjes Constants and Li's Numbers

2004/06/16 by K. Maślanka, Maslanka, Krzysztof
Mathematics · Physics and Astronomy · #11M26 #Advanced Mathematical Identities #Advanced Mathematical Theories #Advanced Mathematical Theories and Applications #FOS: Mathematics #Number Theory (math.NT) #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.math/0406312

openalex publication_date 2004/06/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

In this paper we present a new formula relating Stieltjes numbers γ_n and Laurent coefficinets η_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∼λ_n which are connected with the Riemann hypothesis.

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