Записки научных семинаров Тульской школы теории чисел. Вып. 1. 2022 г.

Тульская школа теории чисел 43 NOTES OF SCIENTIFIC SEMINARS OF THE TULA SCHOOL OF NUMBER THEORY Issue 1. UDC 51(091) DOI 10.22405/2226-8383-2022-1-42-54 Tula School of Number Theory 2 Rebrova Irina Yuryevna — candidate of physical and mathematical Sciences, Tula State Lev Tolstoy Pedagogical University (Tula). e-mail: i_rebrova@mail.ru Chubarikov Vladimir Nikolaevich — doctor of physical and mathematical sciences, professor, Lomonosov Moscow State University (Moscow). e-mail: chubarik2020@mail.ru Abstract The paper presents many unknown facts from the history of the Tula school of number theory. It is shown that the main role in the revival of the Tula school of number theory was played by professors N. M. Korobov, V. I. Nechaev, S. B. Stechkin, and N. M. Dobrovolsky. The role of these main participants in the revival of the scientific school of number theory in Tula is revealed. Various details of the relationship between these participants in the process of reviving the Tula school of number theory are given. To characterize the activities of the Tula scientific school on number theory after its revival, an overview of the main directions of its work over the past 45 years and a brief description of the work done is provided. The article provides a bibliography of the main scientific publications on the number-theoretic method in approximate analysis by N. M. Korobov and N. M. Dobrovolsky, on which the revival of the Tula school of number theory and its subsequent functioning over the past 45 years were based. Keywords: N. M. Korobov, V. I. Nechaev, S. B. Stechkin, N. M. Dobrovolsky, the Tula school of number theory, numerical-theoretic method in approximate analysis, lattices, grids, quadrature formulas, interpolation formulas, hyperbolic Zeta function of lattices, Zeta functions of monoids of natural numbers, uniform distribution, metric space of lattices, smooth variety of lattices, approximation of algebraic numbers. Bibliography: 14 title. For citation: I. Yu. Rebrova, V. N. Chubarikov, 2022, "Tula School of Number Theory" , Notes of scientific seminars of the Tula School of Number Theory , Iss. 1, pp. 42–54. 2 The study was carried out within the framework of state task No. 073-03-2022-117/7 on the topic "Number- theoretic methods in approximate analysis and their applications in mechanics and physics" .