 
Summary: Multiple zeta values at nonpositive integers
Shigeki Akiyama and Yoshio Tanigawa
Abstract. Values of EulerZagier's multiple zeta function at nonpositive integers
are studied, especially at (0, 0, . . . , n) and (n, 0, . . . , 0). Further we prove a
symmetric formula among values at nonpositive 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 zetafunction (s) is that
(2n) = (1)n+1 22n1B2n
(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
