On the enumeration of polynomials with prescribed factorization pattern期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

按检索

On the enumeration of polynomials with prescribed factorization pattern

Institution:	1. Dipartimento di Matematica, Informatica ed Economia, Università degli Studi della Basilicata, Viale dell''Ateneo Lucano 10, 85100 Potenza, Italy;2. School of Mathematical Sciences, The University of Adelaide, Adelaide, South Australia, 5005, Australia;1. Institute of Mathematics, State Academy of Sciences, Pyongyang, Democratic People''s Republic of Korea;2. PGItech Corp., Pyongyang, Democratic People''s Republic of Korea;3. Department of Mathematics, University of Paris VIII, F-93526 Saint-Denis, France;4. University Sorbonne Paris Cité, LAGA, UMR 7539, CNRS, 93430 Villetaneuse, France;5. Telecom Paris, Polytechnic Institute of Paris, 91120 Palaiseau, France

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.

Keywords:	Finite fields Irreducible polynomials Factorization Smooth polynomials
本文献已被 ScienceDirect 等数据库收录！