Converting of algebraic Diophantine equations to a diagonal form with the help of generalized integer orthogonal transformation, maintaining the asymptotic behavior of the number of its integer solutions

2017/04/07 by Victor Volfson, Volfson, Victor
Mathematics · #11D45 #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11D45

paper · pdf · doi:10.48550/arxiv.1704.02238

23 pages

arxiv created 2017/04/07 · arxiv updated 2017/04/10

Abstract

The paper presents a new generalized integer orthogonal transformation which consists of a well known orthogonal transform followed by stretching the basis vectors maintaining the asymptotic behavior of the number of integer solutions for algebraic Diophantine equation. The author shows the properties of this transformation and he receives the algorithm for finding the matrix elements of a generalized integer orthogonal transformation for algebraic Diophantine equation of the second order to diagonal form. The article includes examples illustrating the reduction of algebraic equations of the second order to the diagonal form with the help of integer generalized orthogonal transformation and of determination asymptotics behavior of integer solutions for these equations.

Related

• Converting of algebraic Diophantine equations to a diagonal form with the help of an integer non-orthogonal transformation, maintaining the asymptotic behavior of the number of its integer solutions
• Integer conversions and estimation of the number of integer solutions of algebraic Diophantine equations
• Estimating of the number of natural solutions of homogeneous algebraic Diophantine diagonal equations with integer coefficients
• Estimating of the number of integer (natural) solutions of inhomogeneous algebraic Diophantine diagonal equations with integer coefficients
• Integer Algorithms to Solver Diophantine Linear Equations and Systems