MZV’s as logarithms and applications


Jeng-Daw Yu  ( National Taiwan University )
2017-10-13  13:00 - 14:00
Room 103, Mathematics Research Center Building (ori. New Math. Bldg.)

In these two decades, there are fast developments on classical multiple zeta values (MZV’s) and now MZV’s form a popular research topic in number theory. In his 2004 Inventiones paper, Furusho used the point of view of analytic continuation of p-adic multiple polylogarithms to define p-adic MZV’s. There is a conjecture asserting that p-adic MZV’s satisfy the linear relations that their corresponding real-valued MZV’s satisfy. The purpose of this talk is to give a positive answer of the function field analogue of the conjecture above. Inspired by Furusho’s definition, we use analytic continuation of v-adic Carlitz multiple star polylogarithms to define v-adic MZV’s over function fields in positive characteristic. The key ingredient of the proof is to show the existence of logarithmic interpretations for these v-adic MZV’s and Thakur’s MZV’s, and to use Yu’s sub-t-module theorem (analogue of Wustholz’s analytic subgroup theorem). This is a joint work with Y. Mishiba.