Multiple zeta functions and polylogarithms over global function fields

Abstract

. In [Tha04] Thakur defines function field analogs of the classical multiple zeta function, namely, ζ d ( F q [ T ]; s 1 ,...,s d ) and ζ d ( K ; s 1 ,...,s d ), where K is a global function field. Star versions of these functions were further studied by Masri [Mas06]. We prove reduction formulas for these star functions, extend the construction to function field analogs of multiple polylogarithms, and exhibit some formulas for multiple zeta values.