Frobenius Distributions of Drinfeld Modules of Any Rank Original Research Article

Let A=imageq[T], and let φ be a Drinfeld A-module of rank rgreater-or-equal, slanted2 over imageq(T). For each prime imageset membership, variantA which is a prime of good reduction for φ, let aimage(φ) be the trace of the Frobenius endomorphism at image. We study in this paper the distribution of the traces aimage(φ), and we show that for any tset membership, variantA and any positive integer k, the set of primes imageset membership, variantA of degree k such that aimage(φ)=t has density 0. Our proof is based on a similar result that was obtained by Serre [16] for elliptic curves over image.