# Ein Summierungsverfahren für die Riemannsche ζ-Reihe

@article{HasseEinSF,
title={Ein Summierungsverfahren f{\"u}r die Riemannsche $\zeta$-Reihe},
author={Helmut Hasse},
journal={Mathematische Zeitschrift},
volume={32},
pages={458-464}
}
• H. Hasse
• Mathematics
• Mathematische Zeitschrift
59 Citations
Three Notes on Ser's and Hasse's Representations for the Zeta-functions
This paper shows that the famous Hasse's series for the zeta-function is equivalent to an earlier expression given by a little-known French mathematician Joseph Ser in 1926, and shows that there exist numerous series of the same nature. Expand
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This paper considers some infinite series involving the Riemann zeta function. Some examples are set out below
Nouvelles expressions des formules de Hasse et de Hermite pour la fonction Zêta d’Hurwitz
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New results on the Stieltjes constants: Asymptotic and exact evaluation
Abstract The Stieltjes constants γ k ( a ) are the expansion coefficients in the Laurent series for the Hurwitz zeta function about s = 1 . We present new asymptotic, summatory, and other exactExpand
On quotients of Riemann zeta values at odd and even integer arguments
Abstract We show for even positive integers n that the quotient of the Riemann zeta values ζ ( n + 1 ) and ζ ( n ) satisfies the equation ζ ( n + 1 ) ζ ( n ) = ( 1 − 1 n ) ( 1 − 1 2 n + 1 − 1 ) L ⋆ (Expand
A dynamic approach for the zeros of the Riemann zeta function - collision and repulsion
For N ∈ N consider the N -th section of the approximate functional equation
Absolute series for higher Euler constants
Abstract We give families of series for generalized Euler constants of multiple Hurwitz zeta functions in terms of absolute zeta functions of algebraic groups, extending recent work of Kurokawa andExpand
An approximate functional equation for the Riemann zeta function with exponentially decaying error
• Yochay Jerby
• Computer Science, Mathematics
• J. Approx. Theory
• 2021
This paper proves the following approximate functional equation for the Hasse-Sondow presentation, based on a study of the asymptotic properties of the Riemann zeta function. Expand
The asymptotic expansion of a sum appearing in an approximate functional equation for the riemann zeta function
A representation for the Riemann zeta function valid for arbitrary complex s = σ + it is ζ(s) = ∑ ∞ n=0 A(n, s), where A(n, s) = 2 1− 2 n
An introduction to the Bernoulli function
The Bernoulli function $\operatorname{B}(s, v) = - s\, \zeta(1-s, v)$ interpolates the Bernoulli numbers but can be introduced independently of the zeta function. The point of departure is aExpand