On counting polynomials over finite fields
Journal
Proceedings of the American Mathematical Society
Journal Volume
143
Journal Issue
10
Pages
4305-4316
Date Issued
2015
Author(s)
Abstract
We give an asymptotic formula for the proportion of polynomials of a given degree over a finite field which do not have odd degree irreducible factors. In the case of odd characteristic, this leads to an asymptotic formula for certain weighted partition function which describes the major proportion of the fundamental discriminants where the â negativeâ Pell equation cannot be solved. We also extend the results to counting positive divisors over an arbitrary global function field.
Type
journal article