Algebraic independence of arithmetic Drinfeld modular forms at algebraic points


Chieh-Yu Chang

14:10:00 - 15:00:00

101 , Mathematics Research Center Building (ori. New Math. Bldg.)

Let $f$ be an arithmetic Drinfeld modular form of positive weight. We consider $n$ algebraic points $\alpha_{1},\ldots,\alpha_{n}$ on the Drinfeld upper half plane so that $f(\alpha_{i})$ is nonzero for all $i$. We show that the values $f(\alpha_{1}),\ldots,f(\alpha_{n})$ are algebraically independent if and only if the algebraic points $\alpha_{1},\ldots,\alpha_{n}$ are pairwise non-isogenous. This leads to a classification of the isogeny classes of rank $2$ Drinfeld modules via special values of arithmetic Drinfeld modular forms.