On Drinfeld modular forms of higher rank and quasi-periodic functions

TL;DR

This paper introduces a special function on the Drinfeld period domain for higher ranks, explores its functional equations, relations with quasi-periodic functions, and investigates the transcendence of its values at CM points.

Contribution

It extends the concept of false Eisenstein series to higher ranks and analyzes their functional equations and transcendence properties.

Findings

Defined a new special function on the Drinfeld period domain for r≥2.

Established functional equations and relations with quasi-periodic functions.

Proved transcendence results for values at CM points.

Abstract

In the present paper, we introduce a special function on the Drinfeld period domain $\Omega^{r}$ for $r\geq 2$ which gives the false Eisenstein series of Gekeler when $r=2$. We also study its functional equation and relation with quasi-periodic functions of a Drinfeld module as well as transcendence of its values at CM points.