On special values of meromorphic Drinfeld modular forms of arbitrary rank at CM points

TL;DR

This paper introduces meromorphic Drinfeld modular forms of any rank with specific arithmetic properties, studies their special values at CM points, and demonstrates their algebraic independence, generalizing previous rank two results.

Contribution

It generalizes the study of special values of Drinfeld modular forms to arbitrary rank and establishes algebraic independence at CM points.

Findings

Defined new class of meromorphic Drinfeld modular forms with arithmeticity

Proved algebraic independence of special values at CM points

Extended rank two results to arbitrary rank setting

Abstract

In the present paper, we introduce meromorphic Drinfeld modular forms of arbitrary rank equipped with a particular arithmeticity property. We also study their special values at CM points and show the algebraic independence of these values under some conditions. Our results may be seen as a generalization of Chang's results on the special values of arithmetic Drinfeld modular forms in the rank two setting.