Fermat curves over finite fields

DOI10.1016/0022-314X(88)90007-8zbMath0671.14012MaRDI QIDQ1119704

Arnaldo Garcia, José Felipe Voloch

Publication date: 1988

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

zbMATH Keywords

finite fieldWaring's problemFermat curvenumber of rational points

Mathematics Subject Classification ID

Waring's problem and variants (11P05) Rational points (14G05) Special algebraic curves and curves of low genus (14H45) Curves over finite and local fields (11G20) Finite ground fields in algebraic geometry (14G15) Higher degree equations; Fermat's equation (11D41)

Related Items (31)

Bounds for the number of points on curves over finite fields ⋮ Estimates of trigonometric sums over subgroups and some of their applications ⋮ Polynomial Equations in Subgroups and Applications ⋮ ON THE NUMBER OF RATIONAL POINTS OF GENERALIZED FERMAT CURVES OVER FINITE FIELDS ⋮ The curves \(y^ n=f(x)\) over finite fields ⋮ Automorphisms of generalized Fermat curves ⋮ Duality for projective curves ⋮ Greatest common divisors of \(u-1, v-1\) in positive characteristic and rational points on curves over finite fields ⋮ The Waring's problem over finite fields through generalized Paley graphs ⋮ Separable degree of the Gauss map and strict dual curves over finite fields ⋮ Frobenius nonclassicality with respect to linear systems of curves of arbitrary degree ⋮ Arithmetic progressions in multiplicative groups of finite fields ⋮ On a generalization of planar functions ⋮ Holomorphic differentials of generalized Fermat curves ⋮ On a polynomial version of the sum-product problem for subgroups ⋮ Estimates of Gaussian sums ⋮ Differences of subgroups in subgroups ⋮ On a bound of Garcia and Voloch for the number of points of a Fermat curve over a prime field ⋮ Intersections of shifts of multiplicative subgroups ⋮ Linear recurrence relations for binomial coefficients modulo a prime ⋮ RATIONAL POINTS ON SOME FERMAT CURVES AND SURFACES OVER FINITE FIELDS ⋮ Frobenius nonclassicality of Fermat curves with respect to cubics ⋮ Modular periodicity of binomial coefficients ⋮ On Goppa codes and Weierstrass gaps at several points ⋮ A bound for the number of preimages of a polynomial mapping ⋮ Heilbronn's conjecture on Waring's number (mod \(p\)) ⋮ On complete \((N,d)\)-arcs derived from plane curves ⋮ Frobenius nonclassical components of curves with separated variables ⋮ A generalization of a theorem of B. Segre on regular points with respect to an ellipse of an affine Galois plane ⋮ On some generalized Fermat curves and chords of an affinely regular polygon inscribed in a hyperbola ⋮ Fermat curves over finite fields and cyclic subsets in high-dimensional projective spaces

Cites Work

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• Wronskians and linear independence in fields of prime characteristic
• Weierstrass Points and Curves Over Finite Fields
• A new upper bound for Waring's problem (mod p)
• A note on Waring's problem in GF (p)
• On Waring's Problem in GF[p]
• On the Number of Solutions of Some General Types of Equations in a Finite Field

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