Download this article
Download this article For screen
For printing
Recent Issues
Volume 7, Issue 1
Volume 6, Issue 4
Volume 6, Issue 3
Volume 6, Issue 2
Volume 6, Issue 1
Volume 5, Issue 4
Volume 5, Issue 3
Volume 5, Issue 2
Volume 5, Issue 1
Volume 4, Issue 4
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
Ethics and policies
Peer-review process
Statement, 2023
 
Submission guidelines
Submission form
Editorial board
 
Subscriptions
 
ISSN 2576-7666 (online)
ISSN 2576-7658 (print)
Author index
To appear
 
Other MSP Journals
This article is available for purchase or by subscription. See below.
The $\ell$-adic hypergeometric function and associators

Hidekazu Furusho
Vol. 5 (2023), No. 1, 1–29
DOI: 10.2140/tunis.2023.5.1
Abstract

We introduce an ℓ-adic analogue of Gauss’s hypergeometric function arising from the Galois action on the fundamental torsor of the projective line minus three points. Its definition is motivated by a relation between the KZ equation and the hypergeometric differential equation in the complex case. We show two basic properties, analogues of Gauss’s hypergeometric theorem and of Euler’s transformation formula for our ℓ-adic function. We prove them by detecting a connection of a certain two-by-two matrix specialization of even unitary associators with the associated gamma function, which extends the result of Ohno and Zagier.

PDF Access Denied

We have not been able to recognize your IP address 18.97.14.80 as that of a subscriber to this journal.
Online access to the content of recent issues is by subscription, or purchase of single articles.

Please contact your institution's librarian suggesting a subscription, for example by using our journal-recom­mendation form. Or, visit our subscription page for instructions on purchasing a subscription.

You may also contact us at contact@msp.org
or by using our contact form.

Or, you may purchase this single article for USD 40.00:

Keywords
associators, KZ equation, hypergeometric functions.
Mathematical Subject Classification
Primary: 11F80
Secondary: 11M32, 33C05
Milestones
Received: 23 October 2021
Revised: 31 July 2022
Accepted: 29 August 2022
Published: 20 April 2023
Authors
Hidekazu Furusho
Graduate School of Mathematics
Nagoya University
Japan
© 2023 MSP (Mathematical Sciences Publishers).