The normal order of of the divisor-counting function for invariants of rank 2 Drinfeld modules

Abstract

We compute the first and second moments of the divisor-counting function for the Euler-Poincaré characteristic and the trace of Frobenius for the reductions modulo $p$ of a rank 2 Drinfeld module with nontrivial endomorphism ring, as the prime $p$ varies over the primes of ordinary reduction of the Drinfeld module. From these moments we derive the normal order of the number of prime divisors of these invariants.

arXiv comment20 pages

References in corpus (1)

• Drinfeld modules with maximal Galois action on their torsion points