Counting irreducible polynomials with prescribed coefficients over a finite field
Zhicheng Gao, Simon Kuttner, Qiang Wang · arXiv (Cornell University) · 2021
We continue our study on counting irreducible polynomials over a finite field with prescribed coefficients. We set up a general combinatorial framework using generating functions with coefficients from a group algebra which is generated by equivalent classes of polynomials with prescribed coefficients. Simplified expressions are derived for some special cases. Our results extend some earlier results.