A. Vatwani

Cyclicity of Drinfeld modules modulo primes in arithmetic progressions

Let $A=\mathbb{F}_q[T]$ and $K=\mathbb{F}_q(T)$, and let $\phi$ be a Drinfeld $A$-module over $K$ of rank $r\geq 2$. We study the reduction of $\phi$ at primes $\mathfrak{p} \in A$ lying in a prescribed arithmetic progression, for which $\phi(\mathbb{F}_{\mathfrak{p}})$ has at most $r-1$ cyclic components. We obtain as...