On Log-Algebraic Identities for Anderson t-modules and Characteristic p Multiple Zeta Values

2020/07/21 by Green, Nathan, Dac, Tuan Ngo
#11M38 #11R58 #FOS: Mathematics #Number Theory (math.NT) #Primary 11G09 #Secondary 11M32

paper · doi:10.48550/arxiv.2007.11060

Abstract

Based on the notion of Stark units we present a new approach that obtains refinements of log-algebraic identities for Anderson t-modules. As a consequence, we establish a generalization of Chang's theorem on logarithmic interpretations for special characteristic p multiple zeta values (MZV's) and recover many earlier results in this direction. Further, we devise a direct and conceptual way to get logarithmic interpretations for both MZV's and v-adic MZV's. This generalizes completely the work of Anderson and Thakur for Carlitz zeta values.

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