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Multiple zeta values at non-positive integers Shigeki Akiyama and Yoshio Tanigawa
 

Summary: Multiple zeta values at non-positive integers
Shigeki Akiyama and Yoshio Tanigawa
Abstract. Values of Euler-Zagier's multiple zeta function at non-positive integers
are studied, especially at (0, 0, . . . , -n) and (-n, 0, . . . , 0). Further we prove a
symmetric formula among values at non-positive integers.
Key words: Multiple zeta function, Bernoulli numbers, Stirling numbers
1991 Mathematics Subject Classification: Primary 11M41, Secondary 11B68
1 Introduction.
One of remarkable properties of the Riemann zeta-function (s) is that
(2n) = (-1)n+1 22n-1B2n
(2n)!
2n
for positive integers n, due to L. Euler. Here Bm denote the Bernoulli num-
bers defined by
x
ex - 1
=

m=0
Bm

  

Source: Akiyama, Shigeki - Department of Mathematics, Niigata University

 

Collections: Mathematics