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

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

2006-08-20

arxiv.org/abs/math-ph/0608050v2

Physics

Mathematical Physics

24 pages, no figures

Scientific paper

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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