Functional equations for Nielsen polylogarithms

Abstract: The Nielsen polylogarithms $S_{p,q}$ are perhaps the simplest examples of higher depth multiple polylogarithms, but beyond some simple symmetries, relatively little seems to be known about their identities and functional relations. I will report on some joint work with Herbert Gangl, and Danylo Radchenko, wherein we establish that $S_{3,2}$ satisfies the dilogarithm 5-term relation, modulo explicit $\operatorname{Li}_5$ terms. From this we can always extract corresponding results for $S_{3,2}$ whenever a dilogarithm identity is accessible through the 5-term relation. I will also try to give a flavour of some of our results and evaluations in higher weight.

number theory

Audience: researchers in the topic

Japan Europe Number Theory Exchange Seminar

Series comments: The purpose of the Japan Europe Number Theory Exchange Seminar is to give a opportunity for researchers in Japan and Europe to exchange their research projects by giving short talks (30 min). The target audience are researchers of any level in the area of number theory.

Start for Fall 2021: 26th October