Journal Article10.3103/S002713221103003X
Multiple zeta values
62
TL;DR: The definition of multiple zeta values was extended in this paper, and the preservation of the main properties known for multiple zero values in the sense of their classic definition was proved, as well as their properties in general.
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Abstract: The definition of multiple zeta values is extended in the paper. The preservation of the main properties known for multiple zeta values in the sense of their classic definition is proved.
read more
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Citations
The Multiple Zeta Value data mine
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Multi-poly-bernoulli numbers and related zeta functions
Masanobu Kaneko,Hirofumi Tsumura +1 more
TL;DR: In this article, a multi-indexed poly-Bernoulli number interpolation function was proposed, whose values at non-positive integers are linear combinations of multiple zeta values, which can be regarded as the one to be paired up with the -function defined by Arakawa and Kaneko.
References
Values of Zeta Functions and Their Applications
Don Zagier
- 01 Jan 1994
TL;DR: In this article, the authors give a highly idiosyncratic and prejudiced tour of a number of these applications, making no attempt to be systematic, but only to give a feel for some of the ways in which special values of zeta functions interrelate with other interesting mathematical questions.
857
The Algebra of Multiple Harmonic Series
TL;DR: The harmonic algebra h 0/ker ǫ as mentioned in this paper is a non-commutative polynomial algebra whose first multiplication is commutative and associative, and the second multiplication is associative.
524