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

In the present paper, we introduce a special function on the Drinfeld period domain ${\mathrm{\Omega }}^r$ for $r\ge 2$ 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.