On the number of rational points on some families of Fermat curves over finite fields

DOI10.1016/j.ffa.2005.10.003zbMath1127.11042OpenAlexW2169125950MaRDI QIDQ2370639

Marko J. Moisio

Publication date: 29 June 2007

Published in: Finite Fields and their Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.ffa.2005.10.003

zbMATH Keywords

elliptic curveKloosterman sumexponential sumFermat curves

Mathematics Subject Classification ID

Rational points (14G05) Curves over finite and local fields (11G20)

Related Items (10)

Bounds for the number of points on curves over finite fields ⋮ On classical Kloosterman sums ⋮ Reciprocal polynomials and curves with many points over a finite field ⋮ Kloosterman sum identities and low-weight codewords in a cyclic code with two zeros ⋮ On diagonal equations over finite fields ⋮ RATIONAL POINTS ON SOME FERMAT CURVES AND SURFACES OVER FINITE FIELDS ⋮ Some planar monomials in characteristic 2 ⋮ On complete \((N,d)\)-arcs derived from plane curves ⋮ On some generalized Fermat curves and chords of an affinely regular polygon inscribed in a hyperbola ⋮ On certain diagonal equations over finite fields

Cites Work

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• The number of solutions of certain diagonal equations over finite fields
• Fermat curves over finite fields and cyclic subsets in high-dimensional projective spaces
• A note on multiple exponential sums
• The weights of the orthogonals of the extended quadratic binary Goppa codes
• Explicit evaluation of certain exponential sums.

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