On period polynomials of degree 2^m for finite fields

2016/04/04 by Baoulina, Ioulia N.
#11L05 #11T22 #11T24 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1604.01007

Abstract

We obtain explicit factorizations of reduced period polynomials of degree 2^m, m≥ 4, for finite fields of characteristic p≡ 3 or 5\pmod8. This extends the results of G. Myerson, who considered the cases m=1 and m=2, and S. Gurak, who studied the case m=3.

Related

• The coefficients of the period polynomials
• Gauss periods are minimal polynomials for totally real cyclic fields of prime degree
• On explicit factors of Cyclotomic polynomials over finite fields
• On the generalized Fibonacci sequence of polynomials over finite fields
• Composed Products and Explicit Factors of Cyclotomic Polynomials over Finite Fields