Applied Physics and Mathematics Annotation << Back CONVERTING OF ALGEBRAIC DIOPHANTINE EQUATIONS TO A DIAGONAL FORM WITH GENERALIZED INTEGER ORTHOGONAL TRANSFORMATION, MAINTAINING THE ASYMPTOTIC BEHAVIOR OF THE NUMBER OF ITS INTEGER SOLUTIONS V.L. VOLFSON 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 of algebraic Diophantine equation. The author shows the properties of this transformation. The author received the algorithm for finding the matrix elements of a generalized orthogonal transformation converting algebraic Diophantine equation of the second order to diagonal form and showed the cases when algebraic equation can be reduced to diagonal form with the help of the generalized integer orthogonal transformation. The article includes examples illustrating the reduction of algebraic equations of the second order to the diagonal form with integer generalized orthogonal transformation and determining the asymptotic behavior of integer solutions for these equations. Keywords: algebraic Diophantine equation, diagonal form, asymptotic estimate of the number of integer solutions, generalized integer orthogonal transformation, rotation matrix. Contacts: E-mail: znakvicvolf@mail.ru Pp. 074-083.