Newton polygons, successive minima, and different bounds for Drinfeld modules of rank $2$
Newton polygons, successive minima, and different bounds for Drinfeld modules of rank $2$
Let $K = \mathbb {F}_q(T)$. For a Drinfeld $A$-module $\phi$ of rank $2$ defined over $C_\infty$, there are an associated exponential function $e_\phi$ and lattice $\Lambda _\phi$ in $C_\infty$ given by uniformization over $C_\infty$. We explicitly determine the Newton polygons of $e_\phi$ and the successive minima of $\Lambda _{\phi }$. …