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

Yen-Tsung Chen; Oğuz Gezmiş

paper

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

arXiv:2101.11819

Abstract

In the present paper, we introduce a special function on the Drinfeld period domain $Ω^{r}$ 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.

28 pages. Final version to appear in Transactions of the American Mathematical Society