On generalized Markoff-Hurwitz-type equations over finite fields

DOI10.1007/s10440-010-9568-4zbMath1218.11038OpenAlexW2005039466MaRDI QIDQ607694

Wei Cao

Publication date: 3 December 2010

Published in: Acta Applicandae Mathematicae (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10440-010-9568-4

zbMATH Keywords

Gauss sumfinite fieldsaugmented degree matrixMarkoff-Hurwitz type equations

Mathematics Subject Classification ID

Counting solutions of Diophantine equations (11D45) Polynomials over finite fields (11T06) Other character sums and Gauss sums (11T24) Congruences in many variables (11D79)

Related Items (7)

On the density of integer points on generalised Markoff-Hurwitz and Dwork hypersurfaces ⋮ Counting roots of fully triangular polynomials over finite fields ⋮ A problem of Carlitz and its generalizations ⋮ Degree matrices and enumeration of rational points of some hypersurfaces over finite fields ⋮ ON THE DISTRIBUTION OF POINTS ON THE GENERALIZED MARKOFF–HURWITZ AND DWORK HYPERSURFACES ⋮ Smith normal form of augmented degree matrix and its applications ⋮ Counting solutions to generalized Markoff-Hurwitz-type equations in finite fields

Cites Work

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• Modular counting of rational points over finite fields
• On the number of solutions of the equation \(a_1x_1^{m_1} + \cdots +a_nx_n^{m_n} = bx_1 \cdots x_n\) in a finite field
• On the equation \(x_1^{m_1}+\cdots + x_n^{m_n} = ax_1 \cdots x_n\) over a finite field
• Generalizations of the Markoff-Hurwitz equations over finite fields
• Certain special equations in a finite field
• 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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