Title: New results concerning power series expansions of the Riemann xi function and the Li/Keiper constants
Abstract:The Riemann hypothesis is equivalent to the Li criterion governing a sequence of real constants that are certain logarithmic derivatives of the Riemann xi function evaluated at unity. A new representa...The Riemann hypothesis is equivalent to the Li criterion governing a sequence of real constants that are certain logarithmic derivatives of the Riemann xi function evaluated at unity. A new representation of λ k is developed in terms of the Stieltjes constants γ j and the subcomponent sums are discussed and analysed. Accompanying this decomposition, we find a new representation of the constants η j entering the Laurent expansion of the logarithmic derivative of the Riemann zeta function about s =1. We also demonstrate that the η j coefficients are expressible in terms of the Bernoulli numbers and certain other constants. We determine new properties of η j and σ j , where are the sums of reciprocal powers of the non-trivial zeros of the Riemann zeta function.Read More
Publication Year: 2008
Publication Date: 2008-01-08
Language: en
Type: article
Indexed In: ['crossref']
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Cited By Count: 19
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