The distribution of irreducible polynomials in \(\mathbb{F}_q[t]\)

DOI10.1006/jnth.1996.0139zbMath0923.11163OpenAlexW2031218797MaRDI QIDQ678400

Chih-Nung Hsu

Publication date: 17 April 1997

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jnth.1996.0139

zbMATH Keywords

arithmetic progressionasymptotic formulaexistence of irreducibles of low degreenumber of monic irreduciblesprescribed Artin symbol

Mathematics Subject Classification ID

Polynomials over finite fields (11T06)

Related Items (17)

Counting irreducible polynomials with prescribed coefficients over a finite field ⋮ Weight of irreducible polynomials with coefficients in a finite field ⋮ Enumeration of self-reciprocal irreducible monic polynomials with prescribed leading coefficients over a finite field ⋮ On divisors of sums of polynomials ⋮ On the enumeration of irreducible polynomials over \(\mathrm{GF}(q)\) with prescribed coefficients ⋮ New estimates and existence results about irreducible polynomials and self-reciprocal irreducible polynomials with prescribed coefficients over a finite field ⋮ Self-reciprocal irreducible polynomials with prescribed coefficients ⋮ Irreducible polynomials over \(\mathbb{F}_{2^r}\) with three prescribed coefficients ⋮ Irreducible polynomials with consecutive zero coefficients ⋮ Squarefree polynomials with prescribed coefficients ⋮ Irreducible polynomials with several prescribed coefficients ⋮ On an elementary density problem for polynomials over finite fields ⋮ On the existence of absolutely simple abelian varieties of a given dimension over an arbitrary field ⋮ On Carmichael polynomials ⋮ Applications of the large sieve inequality for \(\mathbb{F}_q[T\)] ⋮ A generalization of the Hansen-Mullen conjecture on irreducible polynomials over finite fields ⋮ Explicit theorems on generator polynomials

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