Number of points on the projective curves \(aY^l=bX^l+cZ^l\) and \(aY^{2l}=bX^{2l}+cZ^{2l}\) defined over finite fields, \(l\) an odd prime

DOI10.1006/jnth.1999.2382zbMath0955.11017OpenAlexW2021260936WikidataQ114234194 ScholiaQ114234194MaRDI QIDQ1125408

S. A. Katre, N. Anuradha

Publication date: 14 February 2000

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

Full work available at URL: https://doi.org/10.1006/jnth.1999.2382

zbMATH Keywords

finite fieldsrational pointscyclotomic numbersJacobi sumsprojective curvesHasse-Weil theorem

Mathematics Subject Classification ID

Arithmetic ground fields for curves (14H25) Curves over finite and local fields (11G20) Other character sums and Gauss sums (11T24) Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture) (14G10) Cyclotomy (11T22)

Related Items

Explicit lifts of quintic Jacobi sums and period polynomials for \(\mathbb F_q\) ⋮ Number of points on certain hyperelliptic curves defined over finite fields ⋮ Cyclotomic problem, Gauss sums and Legendre curve ⋮ Cyclotomic Numbers and Jacobi Sums: A Survey ⋮ Zeta function of the projective curve \(aY^{2l}= bX^{2l}+ cZ^{2l}\) over a class of finite fileds, for odd primes ⋮ Some notes on the linear complexity of Sidel'nikov-Lempel-Cohn-Eastman sequences

Cites Work

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• Jacobsthal sums of prime order
• Uniform cyclotomy
• Complete solution of the cyclotomic problem in $F_q$ for any prime modulus $l, q = p^α, p ≡ 1 (mod l)$
• The cyclotomic numbers of order twelve
• Pure Gauss sums over finite fields
• Jacobi sums and cyclotomic numbers for a finite field
• Cyclotomic numbers of order 2l, l an odd prime
• Numbers of solutions of equations in finite fields