About the number of primitive non-associated second order matrices of determinant \(n\) divisible by a given matrix

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Home Editorial board Publication ethics Peer review guidelines Current Archive Rules for authors Send an article Contacts Address: Vatutina st. 53, Vladikavkaz, 362025, RNO-A, Russia Phone: (8672)23-00-54 E-mail: rio@smath.ru	DOI: 10.23671/VNC.2015.2.7284 About the number of primitive non-associated second order matrices of determinant \(n\) divisible by a given matrix Pachev U. M. Vladikavkaz Mathematical Journal 2015. Vol. 17. Issue 2. Abstract: We obtained formulae for the number of primitive non-associated second order matrices of given odd determinant, as well as for the number of such matrices divisible on the right (left) by the given matrix used in questions of representability of integers by indefinite ternary quadratic forms. Keywords: discrete ergidic method, primitive matrix of integers, norm (determinant) of a matrix, divisibility of matrices, non-associated matrices on the right (left) Language: Russian Download the full text For citation: Pachev U. M. About the number of primitive non-associated second order matrices of determinant \(n\) divisible by a given matrix. Vladikavkazskii matematicheskii zhurnal [Vladikavkaz Math. J.], vol. 17, no. 2, pp.62-67. DOI 10.23671/VNC.2015.2.7284 + References 1. Linnik Ju. V. Jergodicheskie Svojstva Algebraicheskih Polej, Izd-vo LGU, 1967. 2. Malyshev A. V., Pachev U. M. Arithmetic of second-order matrices. J. of Soviet Math. [Zap. Nauchn. Sem. LOMI], 1982, vol. 19, no. 2, pp. 1096-1122. 3. Pachev U. M. Representation of integers by isotropic ternary quadratic forms. Izvestiya: Mathematics [Izv. RAN. Ser. Mat.], 2006, vol. 70, no. 3, pp. 587-604. 4. Newman M. Integral Matrices, N.Y.L.: AP, 1972, 224 p. 5. Pachev U. M. O chisle privedennyh celochislennyh binarnyh kvadratichnyh form s usloviem delimosti pervyh kojefficientov, Chebyshevskij Sb., 2003, vol. 4, no.3(7), pp. 92-105. ← Contents of issue


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