Primitive free cubics with specified norm and trace

DOI10.1090/S0002-9947-03-03301-4zbMath1022.11064OpenAlexW1818952527MaRDI QIDQ4806473

Stephen D. Cohen, Sophie Huczynska

Publication date: 14 May 2003

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9947-03-03301-4

zbMATH Keywords

normfinite fieldtracecharacter sumssieve methodsnormal basisprimitive elementfree element

Mathematics Subject Classification ID

Polynomials over finite fields (11T06) Other character sums and Gauss sums (11T24) Structure theory for finite fields and commutative rings (number-theoretic aspects) (11T30) Arithmetic functions; related numbers; inversion formulas (11A25)

Related Items (9)

Primitive normal polynomials with the first two coefficients prescribed: a revised \(p\)-adic method ⋮ Primitive normal bases for quartic and cubic extensions: a geometric approach ⋮ Abhyankar's affine arithmetic conjecture for the symmetric and alternating groups ⋮ Primitive normal polynomials with multiple coefficients prescribed: an asymptotic result ⋮ Primitive cubics and quartics with zero trace and prescribed norm ⋮ Primitive polynomials with a prescribed coefficient ⋮ Frobenius nonclassical components of curves with separated variables ⋮ On Katz's bound for the number of elements with given trace and norm ⋮ Explicit theorems on generator polynomials

Cites Work

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• Primitive normal bases with prescribed trace
• Primitivity, freeness, norm and trace
• Estimates for Soto-Andrade sums.
• THE PRIMITIVE NORMAL BASIS THEOREM – WITHOUT A COMPUTER
• Primitive free quartics with specified norm and trace
• Primitive Normal Bases for Finite Fields
• Bases for Finite Fields
• Primitive Roots in a Finite Field

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