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Summation properties of the and Li constants

✍ Scribed by Mark W. Coffey

Book ID
104006652
Publisher
Elsevier Science
Year
2009
Tongue
English
Weight
440 KB
Volume
233
Category
Article
ISSN
0377-0427

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✦ Synopsis

We find new summatory and other properties of the constants Ξ· 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.

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