Distribution of the trace of Frobenius on average for rank 2 Drinfeld modules

Abstract

Let $q$ be an odd prime power, $a\in {\mathbb{F}}_q[T]$ and $u\in {\mathbb{F}}_q^{\ast }$. Provided $q\ge 17$, we compute the average number of primes $p$ for which the characteristic polynomial of the Frobenius at $p$ is $X^2-aX+up$ over a family of rank 2 Drinfeld ${\mathbb{F}}_q[T]$-modules. Our results give asymptotic formulas in the $x$-limit.

arXiv comment20 pages

References in corpus (1)

• The Lang-Trotter Conjecture on Average