A VARIATION OF EULER'S APPROACH TO VALUES OF THE RIEMANN ZETA FUNCTION

By Masanobu Kaneko, N. Kurokawa, M. Wakayama. 2002

83 citations recorded by the source corpus.

An elementary method of computing the values at negative integers of the Riemann zeta function is presented. The principal ingredient is a new q-analogue of the Riemann zeta function. We show that for any argument other than 1 the classical limit of this q-analogue exists and equals the value of the Riemann zeta.

Subfields: Algebra and Number Theory, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/6373013b098001c32c064a3cf340c3d4332aaa0d

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

1. U. Kühn
2. Henrik Bachmann
3. Jianqiang Zhao
4. David M. Bradley
5. J. Okuda
6. Michael E. Hoffman
7. Yoshihiro Takeyama

In Geometry and Topology

1. U. Kühn
2. Henrik Bachmann
3. Jianqiang Zhao

Citations in the corpus

• Multiple q-zeta functions and multiple q-polylogarithms (2003, methodology): “By the same argument as in [5], setting the incomplete beta integrals bt(α, β) = ∫ t”
• The algebra of generating functions for multiple divisor sums and applications to multiple zeta values (2013, methodology): “fill a lot of relations from which one can deduce relations of MZV due to the limiting process. It seems strange to us, that albeit the cases (1−q)s[s] have been treated as q-zeta values [Zu], [Pu] or [KKW] the definition (6.1) has become standard (see e.g. [Br], [Zh],[OKZ]) and not (1− q)s1+,...,s k[”