Ein Summierungsverfahren für die Riemannsche ζ-Reihe

  title={Ein Summierungsverfahren f{\"u}r die Riemannsche $\zeta$-Reihe},
  author={Helmut Hasse},
  journal={Mathematische Zeitschrift},
  • H. Hasse
  • Published 1 December 1930
  • Mathematics
  • Mathematische Zeitschrift

Euler-Hurwitz series and non-linear Euler sums

In this paper we derive two expressions for the Hurwitz zeta function involving the complete Bell polynomials in the restricted case where q is a positive integer greater than 1. The arguments of the

Double integrals and infinite products for some classical constants via analytic continuations of Lerch’s transcendent

The two-fold aim of the paper is to unify and generalize on the one hand the double integrals of Beukers for ζ(2) and ζ(3), and of the second author for Euler’s constant γ and its alternating analog


. This paper offers a breakthrough in proving the veracity of original Riemann hypothesis, and extends the validity of its method to include the cases of the Dedekind zeta functions, the Hecke

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.

Some infinite series involving the Riemann zeta function

This paper considers some infinite series involving the Riemann zeta function. Some examples are set out below

Note on relations among multiple zeta-star values

In this note, by using several ideas of other researchers, we derive several relations among multiple zeta-star values from the hypergeometric identities of C. Krattenthaler and T. Rivoal.

Representation of functions in series with parameter

We prove a short general theorem which immediately implies some classical results of Hasse, Guillera and Sondow, Paolo Amore, and also Alzer and Richards. At the end we obtain a new representation

On the duality formula for parametrized multiple series

We show that a duality formula for certain parametrized multiple series yields numerous relations among them. As a result, we obtain a new relation among extended multiple zeta values, which is an

A dynamic approach for the zeros of the Riemann zeta function - collision and repulsion.

For $N \in \mathbb{N}$ consider the $N$-th section of the approximate functional equation $$ \zeta_N(s)= \sum_{n =1 }^N B_n(s),$$ where $$ B_n(s)= \frac{1}{2} \left [ n^{-s} + \chi(s) \cdot n^{s-1}

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