Complete solution of the cyclotomic problem in $F_q$ for any prime modulus $l, q = p^α, p ≡ 1 (mod l)$

DOI10.4064/aa-45-3-183-199zbMath0525.12015OpenAlexW1154827690MaRDI QIDQ3039452

S. A. Katre, A. R. Rajwade

Publication date: 1985

Published in: Acta Arithmetica (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/205966

zbMATH Keywords

cyclotomic numbersJacobi sumscyclotomic problemsolutions of diophantine system

Mathematics Subject Classification ID

Quadratic and bilinear Diophantine equations (11D09) Cyclotomy (11T22)

Related Items (12)

Complete solution to cyclotomy of order \(2l^2\) with prime \(l\) ⋮ 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 ⋮ Explicit lifts of quintic Jacobi sums and period polynomials for \(\mathbb F_q\) ⋮ Euler's criterion for eleventh power nonresidues ⋮ Computation of Jacobi sums of orders \(l^2\) and \(2l^2\) with odd prime \(l\) ⋮ 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 ⋮ Complexities of normal bases constructed from Gauss periods ⋮ Davenport and Hasse's theorems and lifts of multiplication matrices of Gaussian periods ⋮ Cyclotomic numbers and primitive idempotents in the ring \(\mathrm{GF}(q)[x/(x^{p^n} - 1)\)] ⋮ Unique determination of cyclotomic numbers of order five

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