A Theorem of Dickson on Irreducible Polynomials

DOI10.2307/2032168zbMath0048.02701OpenAlexW4247061466MaRDI QIDQ5813984

Leonard Carlitz

Publication date: 1952

Full work available at URL: https://doi.org/10.2307/2032168

Mathematics Subject Classification ID

Polynomials over finite fields (11T06)

Related Items (30)

Counting irreducible polynomials with prescribed coefficients over a finite field ⋮ On the number of irreducible polynomials of special kinds in finite fields ⋮ Irreducible polynomials over finite fields. I ⋮ Fibre products of supersingular curves and the enumeration of irreducible polynomials with prescribed coefficients ⋮ Irreducible polynomials over a finite field ⋮ Enumeration of self-reciprocal irreducible monic polynomials with prescribed leading coefficients over a finite field ⋮ Finite noncommutative geometries related to \(\mathbb{F}_p[x\)] ⋮ The number of irreducible polynomials over finite fields with vanishing trace and reciprocal trace ⋮ On the typical rank of elliptic curves over \(\mathbb{Q}(T)\) ⋮ On the enumeration of irreducible polynomials over \(\mathrm{GF}(q)\) with prescribed coefficients ⋮ On the number of \(N\)-free elements with prescribed trace ⋮ Irreducible polynomials over \(\mathrm{GF}(2)\) with three prescribed coefficients. ⋮ The (2, 3)-generation of the finite 8-dimensional orthogonal groups ⋮ On the reducibility of some composite polynomials over finite fields ⋮ Three proofs of an observation on irreducible polynomials over GF(2) ⋮ Irreducible polynomials over GF(2) with prescribed coefficients. ⋮ Irreducible polynomials over \(\mathbb{F}_{2^r}\) with three prescribed coefficients ⋮ Irreducible polynomials over a finite field and an analogue of Gauss sums over a field of characteristic 2 ⋮ On enumeration of irreducible polynomials and related objects over a finite field with respect to their trace and norm ⋮ The number of irreducible polynomials of degree \(n\) over \(\mathbb F_q\) with given trace and constant terms ⋮ Irreducible polynomials over finite fields with prescribed trace/prescribed constant term ⋮ A new proof of the Hansen-Mullen irreducibility conjecture ⋮ On irreducibles in the polynomial semigroup ⋮ The number of irreducible polynomials over finite fields of characteristic 2 with given trace and subtrace ⋮ Some examples of simply connected dual hyperovals. II. ⋮ Projective characters of extra-special p-groups ⋮ A generalization of the Hansen-Mullen conjecture on irreducible polynomials over finite fields ⋮ Explicit theorems on generator polynomials ⋮ On the number of primitive polynomials over finite fields ⋮ A Note on the Brawley-Carlitz Theorem on Irreducibility of Composed Products of Polynomials over Finite Fields

Cites Work

• The singular series for sums of squares of polynomials

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