Algebraic relations among hyperderivatives of periods and logarithms of Drinfeld modules

Namoijam, Changningphaabi

doi:10.2140/ant.2025.19.1259

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the journal

Ethics and policies

Peer-review process

Submission guidelines

ISSN 1944-7833 (online)

ISSN 1937-0652 (print)

Author index

To appear

Other MSP journals

Algebraic relations among hyperderivatives of periods and logarithms of Drinfeld modules

Changningphaabi Namoijam

Vol. 19 (2025), No. 7, 1259–1311

DOI: 10.2140/ant.2025.19.1259

Abstract

We determine all algebraic relations among all hyperderivatives of the periods, quasiperiods, logarithms, and quasilogarithms of Drinfeld modules defined over a separable closure of the rational function field. In particular, for periods and logarithms that are linearly independent over the endomorphism ring of the Drinfeld module, we prove the algebraic independence of their hyperderivatives and the hyperderivatives of the corresponding quasiperiods and quasilogarithms.

Keywords

Drinfeld modules, Anderson $t$-modules, periods, logarithms, hyperderivatives, algebraic independence

Mathematical Subject Classification

Primary: 11J93

Secondary: 11G09

Milestones

Received: 1 February 2023

Revised: 9 June 2024

Accepted: 3 September 2024

Published: 3 June 2025

Authors

Changningphaabi Namoijam
Department of Mathematics Colby College Waterville, ME United States

Open Access made possible by participating institutions via Subscribe to Open.

Vol. 19, No. 7, 2025