Summation properties of the ηj and Li constants

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:233

Article; Proceedings Paper

Coffey, Mark W.

关键词: Binomial transform;    Li constants;    Riemann zeta function;    Riemann xi function;    Logarithmic derivatives;    Riemann hypothesis;    Li criterion;    Laurent expansion;   

DOI  :  10.1016/j.cam.2009.02.034

来源: Elsevier

【 摘 要 】

We find new summatory and other properties of the constants eta(j) entering the Laurent expansion of the logarithmic derivative of the Riemann zeta function about s = 1. We relate these constants to other coefficients and functions appearing in the theory of the zeta function. In particular, connections to the Li equivalence of the Riemann hypothesis are discussed and quantitatively developed. The validity of the Riemann hypothesis is reduced to the condition of the sublinear order of a certain alternating binomial sum. (C) 2009 Elsevier B.V. All rights reserved.

【 授权许可】

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