Multiple Zeta Values over Global Function Fields
نویسنده
چکیده
Abstract. Let K be a global function field with finite constant field Fq of order q. In this paper we develop the analytic theory of a multiple zeta function Zd(K; s1, . . . , sd) in d independent complex variables defined over K. This is the function field analog of the Euler-Zagier multiple zeta function ζd(s1, . . . , sd) of depth d ([Z1]). Our main result is that Zd(K; s1, . . . , sd) has a meromorphic continuation to all (s1, . . . , sd) in C d and is a rational function in each of q1 , . . . , qd with a specified denominator.
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