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- W2030149666 abstract "The Stieltjes constants gamma_k(a) are the expansion coefficients in the Laurent series for the Hurwitz zeta function about its only pole at s=1. We present the relation of gamma_k(1) to the eta_j coefficients that appear in the Laurent expansion of the logarithmic derivative of the Riemann zeta function about its pole at s=1. We obtain novel integral representations of the Stieltjes constants and new decompositions such as S_2(n) = S_gamma(n) + S_Lambda(n) for the crucial oscillatory subsum of the Li criterion for the Riemann hypothesis. The sum S_gamma(n) is O(n) and we present various integral representations for it. We present novel series representations of S_2(n). We additionally present a rapidly convergent expression for gamma_k= gamma_k(1) and a variety of results pertinent to a parameterized representation of the Riemann and Hurwitz zeta functions." @default.
- W2030149666 created "2016-06-24" @default.
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- W2030149666 date "2007-06-03" @default.
- W2030149666 modified "2023-09-27" @default.
- W2030149666 title "The Stieltjes constants, their relation to the eta_j coefficients, and representation of the Hurwitz zeta function" @default.
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