Title
On the enumeration of polynomials with prescribed factorization pattern
Abstract
We use generating functions over group rings to count polynomials over finite fields with the first few coefficients and a factorization pattern prescribed. In particular, we obtain different exact formulas for the number of monic n-smooth polynomials of degree m over a finite field, as well as the number of monic n-smooth polynomials of degree m with the prescribed trace coefficient.
Year
DOI
Venue
2022
10.1016/j.ffa.2022.102030
Finite Fields and Their Applications
Keywords
DocType
Volume
11T06,11T55,11T23,12Y05
Journal
81
ISSN
Citations 
PageRank 
1071-5797
0
0.34
References 
Authors
0
2
Name
Order
Citations
PageRank
Simon Kuttner101.01
Qiang Wang223737.93