Smith normal form of augmented degree matrix and its applications

DOI10.1016/j.laa.2009.06.018zbMath1184.15012OpenAlexW2010070603MaRDI QIDQ732069

Wei Cao

Publication date: 9 October 2009

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.laa.2009.06.018

zbMATH Keywords

Gauss sumfinite fieldpolynomialSmith normal formaugmented degree matrix

Mathematics Subject Classification ID

Matrices over special rings (quaternions, finite fields, etc.) (15B33) Other character sums and Gauss sums (11T24) Canonical forms, reductions, classification (15A21) Matrices, determinants in number theory (11C20)

Related Items

\(L\)-functions of twisted exponential sums over finite fields ⋮ A refinement of multivariate value set bounds ⋮ Invariant factors of degree matrices and \(L\)-functions of certain exponential sums ⋮ Degree matrices and enumeration of rational points of some hypersurfaces over finite fields ⋮ Smith Normal Form of Augmented Degree Matrix and Rational Points on Toric Hypersurface ⋮ Powers of polynomials and bounds of value sets ⋮ DEGREE MATRICES AND ESTIMATES FOR EXPONENTIAL SUMS OF POLYNOMIALS OVER FINITE FIELDS

Uses Software

• GAP
• Maple
• EDIM

Cites Work

• On generalized Markoff-Hurwitz-type equations over finite fields
• Modular counting of rational points over finite fields
• On the computation of elementary divisors of integer matrices
• The number of solutions of certain equations over a finite field
• Computing Hermite and Smith normal forms of triangular integer matrices
• A Short Proof to Some Results of Sun and Wang
• On a class of equations with special degrees over finite fields
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