Multiple zeta functions and polylogarithms over global function fields
نویسندگان
چکیده
منابع مشابه
Multiple Zeta Values over Global Function Fields
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...
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For every positive integer d we define the q-analog of multiple zeta function of depth d and study its properties, generalizing the work of Kaneko et al. who dealt with the case d = 1. We first analytically continue it to a meromorphic function on C with explicit poles. In our Main Theorem we show that its limit when q ↑ 1 is the ordinary multiple zeta function. Then we consider some special va...
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These are the notes from the summer school in Göttingen sponsored by NATO Advanced Study Institute on Higher-Dimensional Geometry over Finite Fields that took place in 2007. The aim was to give a short introduction on zeta functions over finite fields, focusing on moment zeta functions and zeta functions of affine toric hypersurfaces. Along the way, both concrete examples and open problems are ...
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ژورنال
عنوان ژورنال: Journal de Théorie des Nombres de Bordeaux
سال: 2020
ISSN: 2118-8572
DOI: 10.5802/jtnb.1128