On the coefficients of the Baez-Duarte criterion for the Riemann hypothesis and their extensions

2006/08/20 by Mark W. Coffey, Coffey, Mark W.
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Analytic Number Theory Research #FOS: Physical sciences #Mathematical Physics (math-ph) #Mathematics and Applications #math-ph #math.MP

paper · pdf · doi:10.48550/arxiv.math-ph/0608050

24 pages, no figures

openalex publication_date 2006/08/20 · arxiv created 2006/09/07 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We present analytic properties and extensions of the constants ck appearing in the Baez-Duarte criterion for the Riemann hypothesis. These constants are the coefficients of Pochhammer polynomials in a series representation of the reciprocal of the Riemann zeta function. We present generalizations of this representation to the Hurwitz zeta and many other special functions. We relate the corresponding coefficients to other known constants including the Stieltjes constants and present summatory relations. In addition, we generalize the Maslanka hypergeometric-like representation for the zeta function in several ways.

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