Factoring polynomials in finite fields: An application of Lang-Weil to a problem in graph theory

DOI10.1007/BF01453592zbMath0708.05029OpenAlexW2061837947MaRDI QIDQ920103

Nicholas M. Katz

Publication date: 1990

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/164654

zbMATH Keywords

rational pointsGalois theorydirected graphvariety

Mathematics Subject Classification ID

Separable extensions, Galois theory (12F10) Polynomials over finite fields (11T06) Arithmetic ground fields (finite, local, global) and families or fibrations (14D10) Varieties over finite and local fields (11G25) Directed graphs (digraphs), tournaments (05C20)

Related Items (9)

Univariate polynomial factorization over finite fields ⋮ Algebraic Cayley graphs over finite fields ⋮ A new sieve for distinct coordinate counting ⋮ Splitting fields of characteristic polynomials of random elements in arithmetic groups ⋮ Explicit factorization of \(X^{2^m}p^n-1\) over a finite field ⋮ A natural graph of finite fields distinguishing between models ⋮ On some subgroups of the multiplicative group of finite rings ⋮ Polynomial factorisation and an application to regular directed graphs ⋮ Cayley Graphs Generated by Small Degree Polynomials over Finite Fields

Cites Work

• An Estimate for Character Sums
• Diameters and Eigenvalues
• Gauss Sums, Kloosterman Sums, and Monodromy Groups. (AM-116)
• Number of Points of Varieties in Finite Fields

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