A new proof of the Hansen-Mullen irreducibility conjecture

zbMath1448.11212arXiv1604.04023MaRDI QIDQ5377106

Qiang Wang, Aleksandr Tuxanidy

Publication date: 23 May 2019

Full work available at URL: https://arxiv.org/abs/1604.04023

zbMATH Keywords

symmetric functionfinite fielddiscrete Fourier transformirreducible polynomialprimitive polynomialHansen-Mullen conjecture\(q\)-symmetric

Mathematics Subject Classification ID

Numerical methods for discrete and fast Fourier transforms (65T50) Polynomials over finite fields (11T06)

Related Items (3)

Prescribing coefficients of invariant irreducible polynomials ⋮ Characteristic digit-sum sequences ⋮ Squarefree polynomials with prescribed coefficients

Cites Work

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• Linear recurrences and asymptotic behavior of exponential sums of symmetric Boolean functions
• Matrices with prescribed row and column sums
• A generalization of the Hansen-Mullen conjecture on irreducible polynomials over finite fields
• On the number of \(N\)-free elements with prescribed trace
• The number of irreducible polynomials of degree \(n\) over \(\mathbb F_q\) with given trace and constant terms
• Irreducible polynomials over \(\mathrm{GF}(2)\) with three prescribed coefficients.
• Prescribing the binary digits of primes. II
• Irreducible polynomials with consecutive zero coefficients
• Primitive polynomials with a prescribed coefficient
• Irreducible Coefficient Relations
• The Hansen-Mullen primitivity conjecture: completion of proof
• Irreducible polynomials with prescribed trace and restricted norm
• Symmetric Boolean Functions
• Primitive Polynomials Over Finite Fields
• Generators and irreducible polynomials over finite fields
• Distribution of irreducible polynomials of small degrees over finite fields
• $p$-adic formal series and primitive polynomials over finite fields
• PRIMITIVE POLYNOMIALS WITH PRESCRIBED SECOND COEFFICIENT
• A Theorem of Dickson on Irreducible Polynomials
• Irreducible polynomials with several prescribed coefficients
• Proofs from THE BOOK
• Irreducible polynomials with several prescribed coefficients

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