Generating functions for the generalized Li's sums

2014/11/23 by S. K. Sekatskiǐ, Sekatskii, S. K.
Mathematics · #11M06 #Algebraic and Geometric Analysis #Analytic Number Theory Research #FOS: Mathematics #Mathematics and Applications #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1411.6209

openalex publication_date 2014/11/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Recently, in arXiv:1304.7895; Ukrainian Math. J. - 2014.- 66. - P. 371 - 383, we presented the generalized Li's criterion. This is the statement that the sums /lambda_(n, b, /sigma)=Sum_(rho)((1-((/rho+b)/(/rho-b-2*/sigma))ⁿ)), taken over all Riemann xi-function zeroes taking into account their multiplicity (complex conjugate zeroes are to be paired when summing whenever necessary) for any n=1, 2, 3... and any real b>(-/sigma), are non-negative if and only if there are no Riemann function zeroes with Re(b)>/sigma. For any n=1, 2, 3... and any real b

Citations

• The Positivity of a Sequence of Numbers and the Riemann Hypothesis

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