75-th Anniversary of Professor Urusbi Mukhamedovich Pachev
https://doi.org/10.22405/2226-8383-2025-26-1-243-257
Abstract
This article examines the scientific and pedagogical activities of Professor, Doctor of Physical and Mathematical Sciences Urusbi Mukhamedovich Pachev, who made a significant contribution to research on analytical number theory and geometry of numbers. The main periods of the famous scientist’s life are covered.
U. M. Pachev has been working for a long time at the Kabardino-Balkarian State University named after Kh. M. Berbekov, and heads a scientific seminar on number theory.
Continuing the work of Professor A. V. Malyshev, he was the scientific supervisor of four postgraduate students on candidate dissertations.
About the Authors
Viktor Alekseevich BykovskiiRussian Federation
doctor of physical and mathematical sciences, corresponding member of the Russian Academy of Sciences
Vladimir Grigorievich Chirskii
Russian Federation
doctor of physical and mathematical sciences, professor
Vladimir Nikolaevich Chubarikov
Russian Federation
doctor of physical and mathematical sciences, professor
Nikolay Mikhailovich Dobrovolskiy
Russian Federation
doctor of physical and mathematical sciences,
professor
Nikolay Nikolaevich Dobrovolsky
Russian Federation
candidate of physical-mathematical sciences
Irina Yuryevna Rebrova
Russian Federation
candidate of physical and mathematical sciences
Rezuan Auesovich Dokhov
Russian Federation
candidate of physical and mathematical sciences
References
1. Venkov B. A., 1929, “On the Arithmetic of Quaternions. Fifth Communication,” Bulletin of the
2. USSR Academy of Sciences. VII Series. Department of Physical and Mathematical Sciences,
3. No. 7, 607–622.
4. Venkov B. A., 1929, “On the Arithmetic of Quaternions. Fourth Communication,” Bulletin of
5. the USSR Academy of Sciences. VII Series. Department of Physical and Mathematical Sciences,
6. No. 6, 535–562.
7. Venkov B. A., 1929, “On the Arithmetic of Quaternions. Third Communication,” Bulletin of the
8. USSR Academy of Sciences. VII Series. Department of Physical and Mathematical Sciences,
9. No. 5, 489–504.
10. Venkov B. A., 1928, “On the number of classes of binary quadratic forms of negative
11. determinants. Part two,” Bulletin of the USSR Academy of Sciences. Series VII. Department
12. of Physical and Mathematical Sciences, No. 5, 455–480.
13. Venkov B. A., 1928, “On the number of classes of binary quadratic forms of negative
14. determinants. Part one,” Bulletin of the USSR Academy of Sciences. Series VII. Department
15. of Physical and Mathematical Sciences, No. 4, 375–392.
16. Venkov B., 1922, “On the arithmetic of quaternions. (Second communication),” Bulletin of the
17. Russian Academy of Sciences. Series VI, 16, 221–246.
18. Venkov B., 1922, “On the Arithmetic of Quaternions.
19. Dokhov R. A., Pachev U. M., 2021, “On the Number of Primitive Non-Associated Matrices of
20. Third Order of a Given Determinant,” Chebyshev Sb., 22:5, 129–137.
21. Pachev U. M., Isakova M. M., 2020, “On the Number of Cyclic Subgroups of Prime Order in
22. the Group of Diagonal Matrices over a Cycle Field,” Mat. Notes, 107:3, 479–480.
23. Pachev U. M., Shakova T. A., 2019, “On Units of Quaternion Order of an Indefinite Anisotropic
24. Ternary Quadratic Form,” Chebyshev Sb., 20:4, 270–280.
25. Pachev U. M., Dokhov R. A., 2019, “On singular functions in the problem of the weighted
26. number of integer points on multidimensional hyperboloids of a special type,” Mat. Zametki,
27. :2, 278–293.
28. Pachev U. M., 2018, “On the algebra and arithmetic of binomial and Gaussian coefficients,”
29. Chebyshev Sb., 19:3, 257–269.
30. Pachev U. M., Isakova M. M., 2018, “On cyclic subgroups of the general linear group of degree
31. three over a field of characteristic zero,” Vladikavkaz. Mat. J., 20:2, 62–68.
32. Pachev U. M., 2016, “Ergodic Properties of Flows of Integer Points on Some Hyperboloids in
33. Connection with Hypotheses for the Dirichlet L-Function,” Chebyshevskii Sb., 17:1, 171–186.
34. Pachev U. M., Dokhov R. A., 2016, “On the Number of Integer Points with a Divisibility
35. Condition for the First Coordinates on Hyperboloids of a Special Type,” Mat. Notes, 100:6,
36. –886.
37. Dokhov R. A., Pachev U. M., 2015, “On the weighted number of integer points on some
38. multidimensional hyperboloids,” Chebyshevskii sb., 16:3, 219–245.
39. Pachev U. M., 2015, “On the number of primitive non-associated second-order matrices of
40. determinant n divisible by a given matrix,” Vladikavkaz. Mat. J., 17:2, 62–67.
41. Pachev U. M., 2013, “On the distribution of reduced indefinite binary quadratic forms with the
42. condition of divisibility of the first coefficients by residue classes,” Chebyshev Sb., 14:2, 139–150.
43. Pachev U. M., 2010, “A review of studies on the discrete ergodic method in number theory,”
44. Chebyshev Sb., 11:1, 217–233.
45. Pachev U. M., 2007, “On the asymptotics of the number of reduced integer binary quadratic
46. forms with the condition of divisibility of the first coefficients,” Siberian Math. J., 48:2, 376–388.
47. Pachev U. M., 2006, “Representation of integers by isotropic ternary quadratic forms,” Izv.
48. Mat., 70:3, 167–184.
49. Pachev U. M., 1994, “On the number of classes of Gaussian genus whose arithmetic minimum
50. is divisible by the square of a given odd number,” Mat. Zametki, 55:2, 118–127.
51. Zhemukhova M. Z., Pachev U. M., 2011, “Cyclic subgroups of the general linear group of degree
52. two over a field of characteristic zero,” Vladikavkaz. Mat. zh., 13:3, 17–21.
53. Malyshev A. V., Pachev U. M., 1979, “On the representation of integers by positive ternary
54. quadratic forms (a new version of the discrete ergodic method),” Zap. sci. sem. LOMI, 82,
55. –87.
56. Malyshev A. V., Pachev U. M., 1980, “On the arithmetic of second-order matrices,” Zap. sci.
57. sem. LOMI, 93, 41–86.
58. Pachev U. M., Podsypanin E. V., 2019, “Alexander Vasilievich Malyshev and his studies in
59. number theory,” Chebyshevskii sb., 20:3, 27–42.
60. Pachev U. M., Khalilova L. A., 2022, “On the asymptotics of the number of representations of
61. a pair of integers by quadratic and linear forms with a congruential condition,” Mat. Zametki,
62. :5, 726–737.
63. Pachev U. M., Kodzokov A. Kh., Isakova M. M., Nirova M. S., 2025, “On the asymptotics of
64. representations of a pair of integers by a sum of squares and a linear form with a congruence
65. condition of a special type,” Chebyshevskii sbornik, v. 26, issue 1.
66. Grishmanovskaya K. I., Malyshev A. V., Pachev U. M., Fidharova A. M., 1977, “Proof of the
67. Minkowski conjecture on the critical determinant of the domain |𝑥|𝑝 + |𝑦|𝑝 < 1 in the case
68. ⩽ 𝑝 ⩽ 6,” Zap. sci. f. LOMI, 67, 95–107.
69. Karpov A. N., 1986, “On the representation of numbers by integer isotropic quadratic forms,”
70. Zap. sci. sem. LOMI, 151, 66–67.
71.
Review
For citations:
Bykovskii V.A., Chirskii V.G., Chubarikov V.N., Dobrovolskiy N.M., Dobrovolsky N.N., Rebrova I.Yu., Dokhov R.A. 75-th Anniversary of Professor Urusbi Mukhamedovich Pachev. Chebyshevskii Sbornik. 2025;26(1):243-258. (In Russ.) https://doi.org/10.22405/2226-8383-2025-26-1-243-257