Summation properties of the ηj and Li constants
[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.
[发布日期] 2009-12-01 [发布机构]
[效力级别] Proceedings Paper [学科分类]
[关键词] Binomial transform;Li constants;Riemann zeta function;Riemann xi function;Logarithmic derivatives;Riemann hypothesis;Li criterion;Laurent expansion [时效性]
