5 papers
Trivial zeros of zeta functions of type
Simon Rutard, Takeshi Shinohara
In this paper, we investigate the values of zeta functions of root systems at non-positive integer points. In particular, we focus on the zeta functions of type . Sin…
Stirling polynomials and multiple zeta (star) functions at non-positive integers
Yoni Ishii, Takeshi Shinohara
It is known that the values of multiple zeta functions (MZFs) at non-positive integers can be expressed by Bernoulli numbers. This paper gives explicit formulas for the values of M…
Shuffle product for multiple zeta functions
Nao Komiyama, Takeshi Shinohara
In this paper, we investigate the shuffle product relations for Euler-Zagier multiple zeta functions as functional relations. To this end, we generalize the classical partial fract…
Shuffle product of desingularized multiple zeta functions at integer points
Nao Komiyama, Takeshi Shinohara
In this paper, we investigate the ``shuffle-type'' formula for special values of desingularized multiple zeta functions at integer points. It is proved by giving an iterated integr…
Multiple zeta functions at regular integer points
Takeshi Shinohara
We show the recurrence relations of the Euler-Zagier multiple zeta-function which describes the -fold function with one variable specialized to a non-positive integer as a ratio…