On the enumeration of irreducible polynomials over \(\mathrm{GF}(q)\) with prescribed coefficients

DOI10.1016/j.ffa.2019.01.001zbMath1410.11132arXiv1610.06878OpenAlexW2963780320WikidataQ128267425 ScholiaQ128267425MaRDI QIDQ2422160

Robert Granger

Publication date: 18 June 2019

Published in: Finite Fields and their Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1610.06878

zbMATH Keywords

zeta functionsirreducible polynomialsprescribed coefficientsArtin-Schreier curvesbinary Kloosterman sumsprescribed traces

Mathematics Subject Classification ID

Number-theoretic algorithms; complexity (11Y16) Curves over finite and local fields (11G20) Polynomials over finite fields (11T06) Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture) (14G10)

Related Items (6)

Counting irreducible polynomials with prescribed coefficients over a finite field ⋮ Pseudorandom sequences derived from automatic sequences ⋮ Enumeration of self-reciprocal irreducible monic polynomials with prescribed leading coefficients over a finite field ⋮ The number of irreducible polynomials over finite fields with vanishing trace and reciprocal trace ⋮ New estimates and existence results about irreducible polynomials and self-reciprocal irreducible polynomials with prescribed coefficients over a finite field ⋮ Problems in arithmetic topology

Uses Software

• Magma

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