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Bernik, Vasilij Ivanovich
Professor
Doctor of physico-mathematical sciences (1984)
Speciality: 01.01.06 (Mathematical logic, algebra, and number theory)
E-mail: ;
Keywords: algebraic numbers, regular systems.

https://www.mathnet.ru/eng/person21815
List of publications on Google Scholar
https://mathscinet.ams.org/mathscinet/MRAuthorID/199165
https://elibrary.ru/author_items.asp?authorid=964650

Publications in Math-Net.Ru Citations
2025
1. V. I. Bernik, N. I. Kalosha, D. V. Vasilyev, “Benford's law and approximation of logarithms of natural numbers by rational numbers”, Proceedings of the Institute of Mathematics of the NAS of Belarus, 33:1 (2025),  7–14  mathnet
2023
2. V. I. Bernik, A. S. Kudin, A. V. Titova, “Distinction of measures of Haar cylinders in the Dirichlet theorem for the field of p-adic numbers”, Dal'nevost. Mat. Zh., 23:1 (2023),  3–11  mathnet
2022
3. V. I. Bernik, I. A. Korlyukova, A. S. Kudin, A. V. Titova, “Integer polynomials and Minkowski's theorem on linear forms”, Chebyshevskii Sb., 23:1 (2022),  45–52  mathnet 1
2021
4. V. V. Beresnevich, V. I. Bernik, F. Götze, E. V. Zasimovich, N. I. Kalosha, “Contribution of Jonas Kubilius to the metric theory of diophantine approximation of dependent variables”, Journal of the Belarusian State University. Mathematics and Informatics, 3 (2021),  34–50  mathnet 2
2020
5. V. I. Bernik, E. V. Guseva, N. V. Sakovich, “Approximation of real numbers by algebraic numbers and estimates for the Hausdorff dimension”, Tr. Inst. Mat., 28:1-2 (2020),  3–10  mathnet
2019
6. V. I. Bernik, F. Götze, N. I. Kalosha, “Counting algebraic numbers in short intervals with rational points”, Journal of the Belarusian State University. Mathematics and Informatics, 1 (2019),  4–11  mathnet 2
2018
7. V. I. Bernik, N. V. Budarina, A. V. Lunevich, H. O'Donnell, “Distribution of zeros of nondegenerate functions on short cuttings II”, Chebyshevskii Sb., 19:1 (2018),  5–14  mathnet  elib
8. V. I. Bernik, M. A. Zhur, “Complex algebraic numbers in the sets of $\mathbb{C}^2$ of small Lebesgue measure”, Tr. Inst. Mat., 26:1 (2018),  25–30  mathnet
2017
9. V. I. Bernik, A. G. Gusakova, A. S. Kudin, “Upper and lower estimates of the number of algebraic points in short intervals”, Chebyshevskii Sb., 18:4 (2017),  116–127  mathnet
10. V. I. Bernik, N. V. Budarina, A. V. Lunevich, H. O'Donnel, “Distribution of zeros of nondegenerate functions on short cuttings”, Chebyshevskii Sb., 18:4 (2017),  107–115  mathnet
2016
11. V. I. Bernik, O. N. Kemesh, “Upper bound for number of integral polynomials of four degree with given order of discriminants”, Tr. Inst. Mat., 24:2 (2016),  14–19  mathnet
12. V. Bernik, F. Götze, A. Gusakova, “On the distribution of points with algebraically conjugate coordinates in a neighborhood of smooth curves”, Zap. Nauchn. Sem. POMI, 448 (2016),  14–47  mathnet  mathscinet; J. Math. Sci. (N. Y.), 224:2 (2017), 176–198  scopus 6
2015
13. V. I. Bernik, A. G. Gusakova, A. V. Ustinov, “Distribution of algebraic points in domains of small measure and near the surfaces”, Chebyshevskii Sb., 16:3 (2015),  78–94  mathnet  elib
14. N. V. Budarina, V. I. Bernik, H. O'Donnell, “How does the discriminant of integer polynomials depend on the distribution of roots?”, Chebyshevskii Sb., 16:1 (2015),  153–162  mathnet  elib
15. N. V. Budarina, V. I. Bernik, F. Götze, “Effective estimations of the measure of the sets of real numbers in which integer polynomials take small value”, Dal'nevost. Mat. Zh., 15:1 (2015),  21–37  mathnet  elib
16. V. I. Bernik, F. Götze, “Distribution of real algebraic numbers of arbitrary degree in short intervals”, Izv. RAN. Ser. Mat., 79:1 (2015),  21–42  mathnet  mathscinet  zmath  elib; Izv. Math., 79:1 (2015), 18–39  isi  scopus 23
17. N. V. Budarina, D. Dickinson, V. I. Bernik, “Upper bounds for the number of integer polynomials with given discriminants”, Tr. Inst. Mat., 23:2 (2015),  29–36  mathnet
2014
18. V. I. Bernik, A. V. Ustinov, “On the distribution of points on the modular hyperbola”, Dal'nevost. Mat. Zh., 14:2 (2014),  141–155  mathnet 2
19. A. G. Husakova, V. I. Bernik, “The quantity of algebraic numbers with small derivative of the minimal polynomial in a short intervals”, Tr. Inst. Mat., 22:2 (2014),  18–31  mathnet 1
20. N. V. Budarina, V. I. Bernik, H. O'Donnell, “On the relation between a factorization of a polynomial resultant and the frequency of it’s occurence”, Tr. Inst. Mat., 22:2 (2014),  9–17  mathnet
21. V. I. Bernik, D. V. Vasiliev, A. S. Kudin, “On the number of integral polynomials of given degree and bounded height with small value of derivative at root of polynomial”, Tr. Inst. Mat., 22:2 (2014),  3–8  mathnet 3
2013
22. V. I. Bernik, N. Budarina, H. O'Donnell, “On Regular Systems of Real Algebraic Numbers of Third Degree in Short Intervals”, Sovrem. Probl. Mat., 17 (2013),  61–75  mathnet  elib; Proc. Steklov Inst. Math., 282, suppl. 1 (2013), S54–S66  isi  scopus 1
2011
23. V. I. Bernik, V. A. Shlyk, “On representation of natural numbers by sums of algebraic numbers”, Tr. Inst. Mat., 19:1 (2011),  3–11  mathnet
2008
24. O. S. Kukso, V. I. Bernik, E. V. Zorin, “On small values of discriminats of polynomials, the product of linear integer polynomials of $n$-th degree”, Tr. Inst. Mat., 16:2 (2008),  57–62  mathnet  zmath
2007
25. V. Bernik, F. Götze, O. Kukso, “Bad-approximable points and distribution of discriminants of the product of linear integer polynomials”, Chebyshevskii Sb., 8:2 (2007),  140–147  mathnet  mathscinet  zmath 2
26. N. V. Budarina, D. Dickinson, V. I. Bernik, “Simultaneous approximations of real and complex numbers by algebraic numbers of special kind”, Tr. Inst. Mat., 15:1 (2007),  3–9  mathnet
2005
27. V. V. Lebed, V. I. Bernik, “Algebraic points on the plain”, Fundam. Prikl. Mat., 11:6 (2005),  73–80  mathnet  mathscinet  zmath  elib; J. Math. Sci., 146:2 (2007), 5680–5685  scopus 1
28. V. I. Bernik, O. S. Kukso, “Polynomials with small discriminants and regular systems of real algebraic numbers”, Zap. Nauchn. Sem. POMI, 322 (2005),  10–16  mathnet  mathscinet  zmath; J. Math. Sci. (N. Y.), 137:2 (2006), 4612–4616  scopus 1
2002
29. V. V. Beresnevich, V. I. Bernik, D. Ya. Kleinbock, G. A. Margulis, “Metric Diophantine Approximation: The Khintchine–Groshev Theorem for Nondegenerate Manifolds”, Mosc. Math. J., 2:2 (2002),  203–225  mathnet  mathscinet  zmath  isi 67
1997
30. V. I. Bernik, V. N. Borbat, “Joint approximation of zero by values of integer-valued polynomials”, Trudy Mat. Inst. Steklova, 218 (1997),  58–73  mathnet  mathscinet  zmath; Proc. Steklov Inst. Math., 218 (1997), 53–68 5
1994
31. V. I. Bernik, “Diophantine approximations and sets of divergence of some Fourier series”, Dokl. Akad. Nauk, 336:2 (1994),  151–153  mathnet  mathscinet  zmath; Dokl. Math., 49:3 (1994), 471–473
32. V. I. Bernik, I. R. Dombrovskii, “Effective estimates for the measure of sets defined by Diophantine conditions”, Trudy Mat. Inst. Steklov., 207 (1994),  35–41  mathnet  mathscinet  zmath; Proc. Steklov Inst. Math., 207 (1995), 35–40 1
1991
33. V. I. Bernik, É. I. Kovalevskaya, “Two-dimensional extremal surfaces with jointly extremal partial derivatives”, Mat. Zametki, 50:2 (1991),  14–19  mathnet  mathscinet  zmath; Math. Notes, 50:2 (1991), 779–783  isi
1984
34. V. I. Bernik, “A proof of Baker's conjecture in the metric theory of transcendental numbers”, Dokl. Akad. Nauk SSSR, 277:5 (1984),  1036–1039  mathnet  mathscinet  zmath 1
1980
35. V. I. Bernik, B. I. Ptashnic, “A boundary value problem for a system of partial differential equations with constant coefficients”, Differ. Uravn., 16:2 (1980),  273–279  mathnet  mathscinet  zmath
36. V. I. Bernik, “A metric theorem on the simultaneous approximation of a zero by the values of integral polynomials”, Izv. Akad. Nauk SSSR Ser. Mat., 44:1 (1980),  24–45  mathnet  mathscinet  zmath; Math. USSR-Izv., 16:1 (1981), 21–40  isi 20
1979
37. V. I. Bernik, “Exact order of approximation to almost all points of a parabola”, Mat. Zametki, 26:5 (1979),  657–665  mathnet  mathscinet  zmath; Math. Notes, 26:5 (1979), 821–826  isi 2
1977
38. V. I. Bernik, B. I. Ptashnic, B. O. Salyga, “An analogue of the multipoint problem for a hyperbolic equation with constant coefficients”, Differ. Uravn., 13:4 (1977),  637–645  mathnet  mathscinet  zmath 2
39. V. I. Bernik, “Induced extremal surfaces”, Mat. Sb. (N.S.), 103(145):4(8) (1977),  480–489  mathnet  mathscinet  zmath; Math. USSR-Sb., 32:4 (1977), 413–421  isi 1
1974
40. V. I. Bernik, É. I. Kovalevskaya, “Extremal property of some surfaces in $n$-dimensional Euclidean space”, Mat. Zametki, 15:2 (1974),  247–254  mathnet  mathscinet  zmath; Math. Notes, 15:2 (1974), 140–144 5
1972
41. V. I. Bernik, “Asymptotic number of solutions of some systems of diophantine inequalities”, Mat. Zametki, 11:6 (1972),  619–623  mathnet  mathscinet  zmath; Math. Notes, 11:6 (1972), 378–380 1
2022
42. A. I. Shafarevich, A. T. Fomenko, V. N. Chubarikov, A. O. Ivanov, V. G. Chirskii, V. I. Bernik, V. A. Bykovskii, A. I. Galochkin, S. S. Demidov, S. B. Gashkov, A. I. Nizhnikov, A. A. Fomin, E. Deza, A. Ya. Kanel-Belov, N. M. Dobrovolsky, N. N. Dobrovolsky, I. Yu. Rebrova, V. Kh. Salikhov, “Yuri Valentinovich Nesterenko (to the 75th anniversary)”, Chebyshevskii Sb., 23:1 (2022),  10–20  mathnet
2020
43. S. V. Vostokov, Yu. V. Matiyasevich, Yu. V. Nesterenko, V. N. Chubarikov, V. I. Bernik, A. Laurinčikas, V. G. Zhuravlev, V. G. Chirskii, N. M. Dobrovol'skii, U. M. Pachev, F. V. Podsypanin, I. Yu. Rebrova, B. M. Shirokov, N. N. Dobrovol'skii, “Evgeny Vladimirovich Podsypanin”, Chebyshevskii Sb., 21:4 (2020),  425–426  mathnet
2016
44. V. I. Bernik, V. A. Bykovskij, A. I. Galochkin, N. M. Dobrovol'skij, A. V. Zhmuljova, V. H. Salihov, V. G. Chirskij, V. N. Chubarikov, “Nesterenko Yuri Valentinovich (70 anniversary of Yu. V. Nesterenko)”, Chebyshevskii Sb., 17:4 (2016),  211–2210  mathnet  elib
45. V. I. Bernik, F. Götze, “Letter to the editors”, Izv. RAN. Ser. Mat., 80:3 (2016),  184  mathnet  mathscinet  zmath  elib; Izv. Math., 80:3 (2016), 633  isi  scopus
1990
46. V. I. Bernik, I. P. Kubilyus, V. P. Platonov, “All-Union School “Constructive Methods and Algorithms of Number Theory””, Uspekhi Mat. Nauk, 45:2(272) (1990),  230  mathnet 1
1988
47. V. I. Bernik, A. A. Karatsuba, I. P. Kubilyus, V. P. Platonov, D. A. Suprunenko, “Vladimir Gennadievich Sprindzhuk (obituary)”, Uspekhi Mat. Nauk, 43:4(262) (1988),  161–162  mathnet  mathscinet; Russian Math. Surveys, 43:4 (1988), 195–197  isi

Presentations in Math-Net.Ru
1. Âåëè÷èíû äèñêðèìèíàíòîâ â àðõèìåäîâîé è íåàðõèìåäîâîé ìåòðèêàõ
V. I. Bernik
XV International Conference «Algebra, Number Theory and Discrete Geometry: modern problems and applications», dedicated to the centenary of the birth of the Doctor of Physical and Mathematical Sciences, Professor of the Moscow State University Korobov Nikolai Mikhailovich
May 30, 2018 17:30
2. Exact bounds for the number of integer polynomials with bounded discriminants (common paper with N. Budarina and F. Goetze)
V. I. Bernik
Conference in memory of A. A. Karatsuba on number theory and applications, 2015
January 31, 2015 12:00
3. On which value of the height the distribution of algebraic numbers is regular?
V. I. Bernik
Conference in memory of A. A. Karatsuba on number theory and applications
January 31, 2014 17:05   

Organisations