On the coefficients of the Báez-Duarte criterion for the Riemann hypothesis and their extensions
نویسنده
چکیده
We present analytic properties and extensions of the constants ck appearing in the Báez-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 Maślanka hypergeometric-like representation for the zeta function in several ways.
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Báez-Duarte’s Criterion for the Riemann Hypothesis and Rice’s Integrals
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