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Frobenius Distributions of Drinfeld Modules of Any Rank

✍ Scribed by Chantal David

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
141 KB
Volume
90
Category
Article
ISSN
0022-314X

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✦ Synopsis

Let A=F q [T ], and let , be a Drinfeld A-module of rank r 2 over F q (T ). For each prime p # A which is a prime of good reduction for ,, let a p (,) be the trace of the Frobenius endomorphism at p. We study in this paper the distribution of the traces a p (,), and we show that for any t # A and any positive integer k, the set of primes p # A of degree k such that a p (,)=t has density 0. Our proof is based on a similar result that was obtained by Serre [16] for elliptic curves over Q.

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