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алгебраические решётки, метрическое пространство решёток

1. Аkramov, U. А. 1990, “The isolation theorem for forms corresponding to purely real algebraic fields“, Аnaliticheskaya teoriya chisel i teoriya funktsij. 10 Zap. nauchn. sem. LOMI, no. 185, pp. 5–12.

2. Vejl’, G. 1947, Аlgebraicheskaya teoriya chisel [Algebraic number theory], Gosudarstvennoe izdatel’stvo inostrannoj literatury, Moscow, Russia.

3. Delone, B. N. & Faddeev, D. K. 1940, “Theory of irrationalities of the third degree“, Trudy matematicheskogo instituta imeni V.А. Steklova (Proceedings of the Steklov Institute of Mathematics), vol. 11, pp. 3–340.

4. Dobrovol’skaya, L. P., Dobrovol’skij, M. N., Dobrovol’skij, N. M. & Dobrovol’skij, N. N. 2012, “Hyperbolic zeta functions of grids and grids and calculation of optimal coefficients“, Chebyshevskij sbornik, vol. 13, no. 4(44), pp. 4–107.

5. Dobrovol’skij, M. N. 2005, Mnogomernye teoretiko-chislovye setki i reshyotki i ikh prilozheniya [Multidimensional number-theoretic grids and grids and their applications], Izdatel’stvo tul’skogo gosudarstvennogo pedagogicheskogo universiteta im. L. N. Tolstogo, Tula, Russia.

6. Dobrovol’skij, N.M., Rebrova, I.YU. & Roshhenya, А.L. 1998, “Continuity of the hyperbolic zeta function of lattices“, Matematicheskie zametki (Mathematical Notes), vol. 63, no. 4, pp. 522–526.

7. Kassels, D. 1965, Vvedenie v geometriyu chisel, [Introduction to the geometry of numbers], Mir, Moscow, Russia.

8. Korobov, N. M. 2004, Teoretiko-chislovye metody v priblizhennom analize [Numerical-numerical methods in approximate analysis], 2nd ed., MTSNMO, Moscow, Russia.

9. Rebrova, I. YU. “The continuity of the hyperbolic zeta function of the lattices“, Tez. dokl. III Mezhdunar. konf. “Sovremennye problemy teorii chisel” (Abstracts of the report of the III International Conference “Contemporary problems of number theory”), Tula, 1996, p. 119.

10. Rebrova, I. YU. 1998, “The continuity of the generalized hyperbolic zeta lattice function and its analytic continuation“, Izvestiya TulGU. Seriya Matematika. Mekhanika. Informatika, vol. 4, no. 3, pp. 99–108.

11. Rebrova, I. YU. 1999, “The lattice space and the functions on it“, Ph.D. Thesis, Moscow State Pedagogical University, Moscow, Russia.

12. Skubenko, B. F. 1981, “The isolation theorem for decomposable forms of purely real algebraic fields of degree n > 3“, Аnaliticheskaya teoriya chisel i teoriya funktsij. 4 Zap. nauchn. sem. LOMI, no.112, pp. 167–171.

13. Skubenko, B. F. 1982, “To joint approximations of algebraic irrationalities“, Tselochislennye reshetki i konechnye linejnye gruppy, Zap. nauchn. sem. LOMI, pp. 142–154.

14. Skubenko, B. F. 1981, “On the product of n linear forms of n variables“, Trudy MIАN SSSR, no.158, pp. 175–179.

15. Skubenko, B. F. 1987, “Cyclic sets of points and lattices“, Аnaliticheskaya teoriya chisel i teoriya funktsij. 8 Zap. nauchn. sem. LOMI, pp. 151–158.

16. Skubenko, B. F. 1988, “The minima of a decomposable cubic form in three variables“, Аnaliticheskaya teoriya chisel i teoriya funktsij. 9 Zap. nauchn. sem. LOMI, no.168, pp. 151–158.

17. Skubenko, B. F. 1990, “Minima of decomposable forms of degree n of n variables for n > 3“, Modulyarnye funktsii i kvadratichnye formy. 1 Zap. nauchn. sem. LOMI, no.183, pp. 142–154.

18. Trikolich, E. V., & Yushina, E. I. 2009, “Chain fractions for quadratic irrationalities from the field Q(√5)“, Chebyshevskij sbornik, vol. 10, no. 1, pp. 77–94.

19. Frolov, K. K. 1976, “Estimates from above of the error of quadrature formulas on function classes“, DАN SSSR, no.4, pp. 818–821.

20. Frolov, K. K. 1979, “Quadrature formulas on function classes“, Ph.D. Thesis, Computing Center of the Russian Academy of Sciences of the USSR, Moscow, Russia.

21. Shmeleva, T. S. 2009, “The continuity of the hyperbolic lattice parameter“, Izvestiya Tul’skogo gosudarstvennogo universiteta. Estestvennye nauki, no.3, pp. 92–100.

22. Shmeleva, T. S. “On the continuity of the hyperbolic parameter of lattices“, Аlgebra i teoriya chisel: sovremennye problemy i prilozheniya, posvyashhennoj pamyati professora Аnatoliya Аlekseevicha Karatsuby: materialy VII Mezhdunarodnoj konferentsii (Algebra and Number Theory: Modern Problems and Applications, dedicated to the memory of Professor Anatoly Alekseevich Karatsuba: materials of the VII International Conference), Tula, 2010, pp. 202–206.

23. Shmeleva, T. S. “Approximation of lattices“, Materialy XII Mezhdunarodnoj konferentsii Аlgebra i teoriya chisel: sovremennye problemy i prilozheniya, posvyashhennoj vos’midesyatiletiyu professora Viktora Nikolaevicha Latysheva (Materials of the XII International Conference Algebra and Number Theory: Contemporary Problems and Applications, dedicated to the eightieth birthday of Professor Viktor Nikolaevich Latyshev), Tula, 2014, pp. 311–314.

24. Shmeleva, T. S. “Approximation of gratings and their application“, Materialy XIII Mezhdunarodnoj konferentsii Аlgebra,teoriya chisel i diskretnaya geometriya: sovremennye problemy i prilozheniya, posvyashhennoj vos’midesyatipyatiletiyu so dnya rozhdeniya professora Sergeya Sergeevicha Ryshkova (Materials of the XIII International Conference Algebra, Number Theory and Discrete Geometry: Modern Problems and Applications, dedicated to the eightieth anniversary of the birth of Professor Sergey Sergeevich Ryshkov), Tula, 2015, pp. 384–386.