Download this article
Download this article For screen
For printing
Recent Issues
Volume 4, Issue 3
Volume 4, Issue 2
Volume 4, Issue 1
Volume 3, Issue 4
Volume 3, Issue 3
Volume 3, Issue 2
Volume 3, Issue 1
Volume 2, Issue 4
Volume 2, Issue 3
Volume 2, Issue 2
Volume 2, Issue 1
Volume 1, Issue 4
Volume 1, Issue 3
Volume 1, Issue 2
Volume 1, Issue 1
The Journal
About the Journal
Editorial Board
Subscriptions
 
Submission Guidelines
Submission Form
Policies for Authors
Ethics Statement
 
ISSN (electronic): 2576-7666
ISSN (print): 2576-7658
Author Index
To Appear
 
Other MSP Journals
Analytic continuation of multiple polylogarithms in positive characteristic

Hidekazu Furusho

Vol. 4 (2022), No. 3, 559–586
Abstract

The aim of this paper is to propose a method of analytic continuation of the Carlitz multiple (star) polylogarithms to the whole space by using Artin–Schreier equations and present a treatment of their branches by introducing the notion of monodromy modules. As applications of this method, we obtain (1) a method of continuation of the logarithms of higher tensor powers of the Carlitz module, (2) the orthogonal property (Chang–Mishiba functional relations), (3) a branch independency of the Eulerian property.

Keywords
(t-motivic) Carlitz (multiple) (star) polylogarithm, Carlitz module, t-module
Mathematical Subject Classification
Primary: 11R58, 33E50
Milestones
Received: 29 November 2021
Revised: 3 February 2022
Accepted: 19 February 2022
Published: 9 November 2022
Authors
Hidekazu Furusho
Graduate School of Mathematics
Nagoya University
Chikusa-ku
Chikusaku, Nagoya 464-8602
Japan