On period polynomials of degree $2^m$ for finite fields

Ioulia N. Baoulina

On period polynomials of degree $2^m$ for finite fields

Number Theory 2016-04-05 v1

Authors: Ioulia N. Baoulina

Abstract

We obtain explicit factorizations of reduced period polynomials of degree $2^m$ , $m\ge 4$ , for finite fields of characteristic $p\equiv 3$ or $5\pmod{8}$ . This extends the results of G. Myerson, who considered the cases $m=1$ and $m=2$ , and S. Gurak, who studied the case $m=3$ .

Keywords

period polynomials finite fields factorization reduced period polynomials characteristic p explicit formulas

Cite

@article{arxiv.1604.01007,
  title  = {On period polynomials of degree $2^m$ for finite fields},
  author = {Ioulia N. Baoulina},
  journal= {arXiv preprint arXiv:1604.01007},
  year   = {2016}
}

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16 pages

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