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ANDREI BORISOVICH SHIDLOVSKII

https://doi.org/10.22405/2226-8383-2015-16-3-6-34

Abstract

The authors set themselves two main objectives: to characterize the main stages of life of a Lomonosov Moscow State University professor Andrei Borisovich Shydlovsky and give a brief analysis of his scientific and educational activities, which had a significant impact on the development of scientific schools in the field of the theory of transcendental numbers, where he was one of the leading national experts and organizer of international scientific conferences in this area. Among his students 15 defended their dissertations and three of them later became doctors of physical and mathematical sciences. Professor Shidlovskii studies on the theory of transcendental numbers are emphasized.

 

About the Authors

A. I. Galochkin
Московский государственный университет имени М. В. Ломоносова
Russian Federation


Yu. V. Nesterenko
Московский государственный университет имени М. В. Ломоносова
Russian Federation


V. G. Chirskiy
Московский государственный университет имени М. В. Ломоносова
Russian Federation


V. I. Salikhov
Брянский государственный технический университет
Russian Federation


References

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2. Shidlovskii, A. B. 1954, "On transcendentality and algebraic independence of the values of entire functions of certain classes" , Dokl. Akad. Nauk SSSR, vol. 96, pp. 697–700. (Russian)

3. Shidlovskii, A. B. 1955, "On a criterion of algebraic independence of the values of a class of entire functions" , Dokl. Akad. Nauk SSSR, vol. 100, pp. 221–224. (Russian)

4. Shidlovskii, A. B. 1955, "On transcendental numbers of certain classes" , Dokl. Akad. Nauk SSSR, vol. 103, pp. 977–980. (Russian)

5. Shidlovskii, A. B. 1955, "On transcendentality of the values of a class of entire functions satisfying linear differential equations" , Dokl. Akad. Nauk SSSR, vol. 105, pp. 35–37. (Russian)

6. Shidlovskii, A. B. 1956, "On a new criterion of the transcendentality and algebraic independence of values assumed by a class of entire functions" , Dokl. Akad. Nauk SSSR, vol. 106, pp. 399–400. (Russian)

7. Shidlovskii, A. B. 1956, "On algebraic independence of transcendental numbers of a certain class" , Dokl. Akad. Nauk SSSR, vol. 108, pp. 400–403. (Russian)

8. Shidlovskii, A. B. 1956, "On one class of transcendental numbers" , Proc. 3rd AllUnion Math. Congr., AN, Moscow, vol. 1, pp. 15–16. (Russian)

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12. Shidlovskii, A. B. 1960, "On the transcendence and algebraic independence of values of the E-functions related to an algebraic equation over the rational function field" , Vestnik Moskov. Univ. Ser. I Mat. Meh., no. 5, pp. 19–28. (Russian)

13. Shidlovskii, A. B. 1961, "A generalization of Lindemann’s theorem" , Dokl. Akad. Nauk SSSR, vol. 138, pp. 1301–1304. (Russian)

14. Shidlovskii, A. B. 1961, "On the transcendence and algebraic independence of the values of certain E-functions" , Vestnik Moskov. Univ. Ser. I Mat. Meh., no. 5, pp. 44–59. (Russian)

15. Shidlovskii, A. B. 1962, "Transcendency and algebraic independence of values of E-functions related by an arbitrary number of algebraic equations over the field of rational functions" , Izv. Akad. Nauk SSSR Ser. Mat., vol. 26, pp. 877– 910. (Russian)

16. Shidlovskii, A. B. 1964, "Transcendence of the values of E-functions" , Proc. 4th All-Union Math. Congr. (Leningrad, 1961), Nauka, Leningrad, vol. II, pp. 147–158. (Russian)

17. Shidlovskii, A. B. 1966, "Transcendence and algebraic independence of values of E-functions satisfying linear nonhomogeneous differential equations of the second order" , Dokl. Akad. Nauk SSSR, vol. 169, pp. 42–45. (Russian)

18. Shidlovskii, A. B. 1966, "Transcendence and algebraic independence of values of E-functions" , Proc. Int. Math. Congr., Moscow, pp. 177–180.

19. Shidlovskii, A. B. 1966, "Transcendence of the values of some classes of functions" , Lit. Mat. Sb., vol. 6, no. 1, pp. 129–130.

20. Shidlovskii, A. B. 1966, "On a general theorem on the algebraic independence of values of E-functions" , Dokl. Akad. Nauk SSSR, vol. 171, pp. 810–813. (Russian)

21. Shidlovskii, A. B. 1967, "On estimates of the measure of transcendentality of the values of E-functions" , Uspehi Mat. Nauk, vol. 22, no. 3 (135), pp. 245– 246. (Russian)

22. Pjateckii-Shapiro, I. I. & Shidlovskii, A. B. 1967, "Aleksandr Osipovic Gel’- fond" , Uspehi Mat. Nauk, vol. 22, no. 3 (135), pp. 247–256. (Russian)

23. Fel’dman, N. I. & Shidlovskii, A. B. 1967, "The development and present state of the theory of transcendental numbers" , Uspehi Mat. Nauk, vol. 22, no. 3 (135), pp. 3–81. (Russian)

24. Shidlovskii, A. B. 1967, "Estimates of the degree of transcendence of the values of E-functions" , Mat. Zametki, vol. 2, no. 1, pp. 33–44. (Russian)

25. Shidlovskii, A. B. 1967, "On estimates of the measure of transcendentality of the values of E-functions" , Proc. 2nd Congr. Bolg. Math., Varna, p. 91.

26. Fel’dman, N. I. & Shidlovskii, A. B. 1967, "Alexander Osipovich Gelfond (on his sixtieth birthday)" , Vestnik Moskov. Univ. Ser. I. Mat. Meh., no. 3, pp. 106– 108. (Russian)

27. Shidlovskii, A. B. 1968, "Transcendentality and algebraic independence of values of E-functions" , Proc. Internat. Congr. Math. (Moscow, 1966), Mir, Moscow, pp. 299–307. (Russian)

28. Shidlovskii, A. B. 1968, "Algebraic independence of the values of certain hypergeometric E-functions" , Trudy Moskov. Mat. Obsh., vol. 18, pp. 55–64. (Russian)

29. Shidlovskii, A. B. 1969, "A. O. Gelfond (obituary)" , Vestnik Moskov. Univ. Ser. I. Mat. Meh., no. 3, pp. 123–125. (Russian)

30. Shidlovskii, A. B. 1969, "A certain theorem of C. Siegel" , Vestnik Moskov. Univ. Ser. I. Mat. Meh., vol. 24, no. 6, pp. 39–42. (Russian)

31. Shidlovskii, A. B. 1969, "On arithmetical nature of the values of one class of functions satisfying linear differential equations" , Proc. Resp. Symp. on Diff. Equations, Odessa Univ., Odessa, pp. 75–76.

32. Bukhshtab A. A. & Shidlovskii, A. B. 1969, "A. O. Gelfond (obituary)" , Mat. v shkole, no. 1, p. 89–90.

33. Fel’dman, N. I. & Shidlovskii, A. B. 1970, "The methods of A. O. Gel’fond in the theory of transcendental numbers" , Uspehi Mat. Nauk, vol. 25, no. 1 (151), pp. 201–202. (Russian)

34. Levin, B. V., Feldman, N. I. & Sidlovski, A. B. 1970, "Alexander O. Gelfond" , Acta Arith., vol. 17, pp. 315–336.

35. Shidlovskii, A. B. 1972, "Some unsolved problems of transcendental number theory" , Proc. All-Union Conf. on Current Problems of Number Theory, Samarkand Gos. Univ., Samarkand, p. 90. (Russian)

36. Shidlovskii, A. B. 1972, "On arithmetical properties of the values of analytical functions from some classes" , Proc. 3rd Congr. Bolg. Math., Varna, vol. I, p. 218.

37. Shidlovskii, A. B. 1972, "The work of P. L. Chebyshev in number theory" , Probl. Ist. Mat. Meh., MGU, Moscow, issue 1, pp. 4–9. (Russian)

38. Shidlovskii, A. B. 1973, "The arithmetic properties of the values of analytic functions" , Proceedings of the International Conference on Number Theory (Moscow, 1971), Trudy Mat. Inst. Steklov, vol. 132, pp. 169–202. (Russian)

39. Shidlovskii, A. B. 1974, "On transcendentality of values of E-functions at algebraic points" , Proc. All-Union Conf. “Problems of Analytical Number Theory and Its Applications”, Vilnius Gos. Univ., Vilnius, pp. 306–309. (Russian)

40. Shidlovskii, A. B. 1974, "On transcendental number theory problems" , Appendix to Collected Translations Book «Theory of Diophantine Approximation Problems», Mir, pp. 139–160. (Russian)

41. Stechkin, S. B., Uzhdaviniss, R. V. & Shidlovskii, A. B. 1975, "All-Union Conference on Problems of Analytical Number Theory and Its Applications" , Uspekhi Mat. Nauk, vol. 30, no. 3, pp. 198–200. (Russian)

42. Shidlovskii, A. B. 1977, "Algebraic number" , Mat. Encycl., Sov. Encycl., Moscow, vol. 1, pp. 195–198. (Russian)

43. Shidlovskii, A. B. 1977, "On algebraic independency of E-functions values at transcendental points" , Proc. All-Union Number Theory School, Tadzhik. Univ., Dushanbe, pp. 135–136. (Russian)

44. Shidlovskii, A. B. 1977, "On the estimates of the transcendentality measure of E-functions values" , Vestnik Moskov. Univ. Ser. I. Mat. Mekh., no. 6, pp. 3– 10.

45. Shidlovskii, A. B. 1977, "The arithmetic properties of values of some classes of analytic functions" , Tagungsbericht 10/1977. Zahlentheorie (Diophantische Approximationen), Mathematisches Forschungsinstitut Oberwolfach, p. 18.

46. Shidlovskii, A. B. 1979, "On the estimates of the algebraic independence measures of the values of E-functions" , J. Austral. Math. Soc. Ser. A, vol. 27, no. 4, pp. 385–407.

47. Shidlovskii, A. B. 1979, "Arithmetic properties of E-function values at algebraic points" , Dokl. Akad. Nauk SSSR, vol. 248, no. 1, pp. 50–55. (Russian) 48. Shidlovskii, A. B. 1979, "Arithmetic properties of the values of analytic functions of certain classes" , Vestnik Moskov. Univ. Ser. I. Mat. Mekh., no. 6, pp. 24–31. (Russian)

48. Shidlovskii, A. B. 1980, "Arithmetic properties of polynomials of values of Efunctions connected with algebraic equations in a field of rational functions" , Acta Arith., vol. 37, pp. 405—426. (Russian)

49. Shidlovskii, A. B. 1980, "On the arithmetic properties of values of E-functions connected with algebraic equations in the rational function field" , Dokl. Akad. Nauk SSSR, vol. 251, no. 4, pp. 808–812. (Russian)

50. Shidlovskii, A. B. 1980, "Estimate of a measure of mutual transcendence of values of E-functions connected by arbitrary algebraic equations over C(z)" , Uspekhi Mat. Nauk, vol. 35, no. 2 (212), pp. 227–228. (Russian)

51. Shidlovskii, A. B. 1981, "Estimates of polynomials from values of E-functions" , Mat. Sb., vol. 115 (157), no. 1, pp. 3—39. (Russian)

52. Shidlovskii, A. B. 1981, "On estimates of polynomials from values of analytical functions" , Proc. Int. Conf. Compl. Anal. and Appl., Varna, p. 78.

53. Shidlovskii, A. B. 1982, "Diofantovy priblizheniya i transtsendentnye chisla" , [Diophantine approximations and transcendental numbers], Moskov. Gos. Univ., Moscow, 264 pp. (Russian)

54. Shidlovskii, A. B. 1983, "Estimates for the moduli of polynomials with algebraic coefficients at the values of E-functions" , Studies in Pure Mathematics, Birkh¨auser, Basel, pp. 635—657, doi: 10.1007/978-3-0348-5438-2_55.

55. Shidlovskii, A. B. 1983, "Arithmetical properties of E-functions values" , Proc. All-Union Conf. Transcendental Number Theory and Its Applications, Mos. Univ., Moscow, pp. 160–162. (Russian)

56. Shidlovskii, A. B. 1983, "The basic lemma of the method of proof of algebraic independence of values of E-functions" , Vestnik Moskov. Univ. Ser. I. Mat. Mekh., no. 6, pp. 94—98. (Russian)

57. Galochkin, A. I., Nesterenko, Yu. V. & Shidlovskii, A. B. 1984, "Vvedenie v teoriyu chisel." , [Introduction to number theory] Moskov. Gos. Univ., Moscow, 148 pp. (Russian)

58. Galochkin, A. I., Fel’dman, N. I. & Shidlovskii, A. B. 1984, "All-Union Conference Transcendental Number Theory and Its Applications , Uspekhi Mat. Nauk, vol. 39, no. 6, pp. 251–252. (Russian)

59. Shidlovskii, A. B. 1984, "On algebraic independence of E-functions values" , Proc. All-Union Conf. Number Theory and Its Applications, Tbilisi Univ., Tbilisi, pp. 290–293. (Russian)

60. Shidlovskii, A. B. 1987, "On the algebraic independence of values of E-functions at algebraic points" , Vestnik Moskov. Univ. Ser. I. Mat. Mekh., no. 1, pp. 30— 33. (Russian)

61. Shidlovskii, A. B. 1987, "On the transcendence and algebraic independence of the values of some classes of analytic functions" , Trudy Mat. Inst. Steklov, vol. 180, pp. 232–234. (Russian)

62. Shidlovskii, A. B. 1987, "Transtsendentnye chisla." , [Transcendental numbers] Nauka, Moscow, 448 pp. (Russian)

63. Aptekarev, A. I., Kozlov, V. V., Olevskii, A. M., Potapov, M. K., Shidlovskii, A. B. & Ul’yanov, P. L. 1987, "In memory of Evgenii Mikhailovich Nikishin" , Vestnik Moskov. Univ. Ser. I. Mat. Mekh., no. 6, pp. 88—91. (Russian)

64. Shidlovsky, A. B. 1988, "On arithmetic properties of the values of E-functions" , New advances in transcendence theory (Durham, 1986), Cambridge Univ. Press, Cambridge, pp. 347—351.

65. Shidlovskii, A. B. 1989, "On the problem of algebraic independence of values of E-functions at algebraic points" , Mat. Zametki, vol. 45, no. 1, pp. 115–122. (Russian)

66. Shidlovskii, A. B. 1989, "A criterion for algebraic independence of the values of an E-function at algebraic points" , Vestnik Moskov. Univ. Ser. I. Mat. Mekh., no. 6, pp. 17–21. (Russian)

67. Shidlovskii, A. B. 1989, "On some problems of algebraic independence of Efunctions values" , Proc. All-Union School Constructive Methods and Number Theory Algorithms, Inst. Mat. AN BSSR, Minsk, p. 167. (Russian)

68. Shidlovskii, A. B. 1989, "On the arithmetical properties of the values of Efunctions" , Proc. Congr. Number Theory (Spanish) (Zarauz, 1984), Univ. Pa´ıs Vasco-Euskal Herriko Unib., Bilbao, pp. 28–42. (Spanish)

69. Shidlovskii, A. B. 1989, "Approximation of algebraic numbers by rationals" , Proc. Congr. Number Theory (Spanish) (Zarauz, 1984), Univ. Pa´ıs Vasco-Euskal Herriko Unib., Bilbao, pp. 138–147. (Spanish)

70. Shidlovskii, A. B. 1989, "Hilbert’s seventh problem" , Proc. Congr. Number Theory (Spanish) (Zarauz, 1984), Univ. Pa´ıs Vasco-Euskal Herriko Unib., Bilbao, pp. 176–180. (Spanish)

71. Shidlovskii, A. B. 1989, "Aproximaciones diof´anticas y n´umeros transcendentes" , [Diophantine approximations and transcendental numbers] Universidad del Pa´ıs Vasco, Bilbao. (Spanish)

72. Shidlovskii, A. B. 1989, "Transcendental numbers" , de Gruyter Studies in Mathematics, vol. 12, Walter de Gruyter & Co., Berlin, xx+466 pp.

73. Nesterenko, Yu. V., Shidlovskii, A. B. & Sorokin, V. N. 1990, "Pade approximation and Diophantine approximations" , appendix for book: Nikishin, Eu. M. Selected topics of mathematical analysis. Reports on mathematics and its applications, vol. 3, issue 1, AN SSSR & Minvuz RSFSR, Moscow, pp. 399–411. (Russian)

74. Shidlovskii, A. B. 1990, "On the transcendence and algebraic independence of the values of E-functions at algebraic points" , Tagungsbericht 40/1990. Diophantische Approximationen, Mathematisches Forschungsinstitut Oberwolfach, p. 16.

75. Arnol’d, V. I., Gorin, E. A., Lin, V. Ya., Nesterenko, Yu. V., Shidlovskii, A. B., Shubin, M. A., Tikhomirov, V. M., Ul’yanov P. L. & Vitushkin, A. G. 1990, "Vyacheslav Alekseevich Oleinikov (obituary)" , Uspekhi Mat. Nauk, vol. 45, no. 1, pp. 163–165. (Russian)

76. Shidlovskii, A. B. 1991, "On algebraic independence of E-functions values" , Proc. Resp. Sci.-Tech. Conf. Number Theory and Its Applications, Tashkent Ped. Inst., Tashkent, p. 136. (Russian)

77. Kubilis, I. P., Nechaev, V. I., Stechkin, S. B. & Shidlovskii, A. B. 1991, "Aleksandr Adol’fovich Bukhshtab" , Uspekhi Mat. Nauk, vol. 46, no. 1 (277), pp. 201–202. (Russian)

78. Shidlovskii, A. B. 1991, "On the algebraic independence of values of Efunctions" , Uspekhi Mat. Nauk, vol. 46, no. 4 (280), pp. 175–176. (Russian)

79. Shidlovskii, A. B. 1992, "On the arithmetic properties of the values of Efunctions" , New trends in probability and statistics, vol. 2, (Palanga, 1991), VSP, Utrecht, pp. 23–29.

80. Shidlovskii, A. B. 1992, "Transcendence of values of a subclass of E-functions" , Uspekhi Mat. Nauk, vol. 47, no. 4(286), pp. 215–216. (Russian)

81. Shidlovskii, A. B. 1992, "Number Theory Department" , Mathematics in Moscow University, Mosc. Univ., Moscow, pp. 84–111. (Russian)

82. Shidlovskii, A. B. 1993, "Transcendence of values of E-functions that are solutions of second-order linear differential equations" , Mat. Sb., vol. 184, no. 5, pp. 75–84. (Russian)

83. Shidlovskii, A. B. 1993, "On linear independence of the values of E-functions at algebraic points" , Proc. Int. Conf. Modern Number Theory Problems, Tula Ped. Univ., Tula, p. 80. (Russian)

84. Shidlovskii, A. B. 1993, "On linear independence of the values of E-functions of algebraic points" , Tagungsbericht 43/1993. Diophantische Approximationen, Mathematisches Forschungsinstitut Oberwolfach, pp. 14–15.

85. Shidlovskii, A. B. 1994, "On the linear independence of values of E-functions at algebraic points" , Mat. Zametki, vol. 55, no. 2, pp. 174–185. (Russian)

86. Shidlovskii, A. B. 1994, "On the algebraic independence of the values of Efunctions connected by algebraic equations over the field of rational functions" , Trudy Mat. Inst. Steklov, vol. 207, pp. 369–376. (Russian)

87. Shidlovskii, A. B. 1995, "On the linear independence of values of E-functions associated with an algebraic equation over the field of rational functions" , Mat. Zametki, vol. 58, no. 5, pp. 794–797. (Russian)

88. Nesterenko, Yu. V. & Shidlovskii, A. B. 1995, "In memory of Naum Il’ich Fel’dman [1918–1994]" , Vestnik Moskov. Univ. Ser. I. Mat. Mekh., no. 6, pp. 108–109. (Russian)

89. Galochkin, A. I., Nesterenko, Yu. V. & Shidlovskii, A. B. "Vvedenie v teoriyu chisel." , [Introduction to number theory] 2nd edition. Mosk. Univ., Moscow, 160 pp. (Russian)

90. Aptekarev, A. I., Kalyagin, V. A., Kozlov, V. V., Potapov, M. K., Sorokin, V. N., Ul’yanov, P. L., Fomenko, A. T. & Shidlovskii, A. B. 1995, "Evgenii Mikhailovich Nikishin" , Vestnik Moskov. Univ. Ser. I. Mat. Mekh., no. 6, pp. 110–111. (Russian)

91. Korobov, N. M., Nesterenko, Yu. V. & Shidlovskii, A. B. "Naum Il’ich Fel’dman" , Uspekhi Mat. Nauk, vol. 50, no. 6 (306), pp. 157–162. (Russian)

92. Nesterenko, Yu. V. & Shidlovskii, A. B. 1996, "On the linear independence of values of E-functions" , Mat. Sb., vol. 187, no. 8, pp. 93–108. (Russian)

93. Shidlovskii, A. B. 1996, "On the linear independence of values of E-functions" , Vestnik Moskov. Univ. Ser. I. Mat. Mekh., no. 4, pp. 53–56. (Russian)

94. Shidlovskii, A. B. 1996, "Criteria for the linear and algebraic dependence of the values of E-functions at algebraic points" , Uspekhi Mat. Nauk, vol. 51, no. 2 (308), pp. 179–180. (Russian)

95. Shidlovskii, A. B. 1996, "Criteria for the linear and algebraic independence of the values of E-functions at algebraic points" , Diophantine Approximations. Mathematical Transactions, vol. 2, Centr Prikl. Issl. Meh.-Mat. Fak. MGU, Moscow, pp. 114–120. (Russian)

96. Shidlovskii, A. B. 1996, "On linear independence of values of E-functions" , Proc. Int. Conf. Modern Number Theory Problems and Its Applications, Tula Ped. Univ., Tula, p. 155. (Russian)

97. Shidlovskii, A. B. 1997, "On the algebraic independence of values of Efunctions" , Tr. Mat. Inst. Steklova, vol. 218, pp. 439–443. (Russian)

98. Shidlovskii, A. B. 1999, "On the arithmetic properties of values of E-functions" , Mat. Zametki, vol. 66, no. 3, pp. 452–458. (Russian)

99. Shidlovskii, A. B. 2000, "On the properties of algebraic equations that connect the set of E-functions over the field of rational functions" , Mat. Zametki, vol. 68, no. 5, pp. 761–770. (Russian)

100. Shidlovskii, A. B. 2003, "Number theory department" , Mathematics in Moscow University on the edge of XXI century, part III, ed. O. B. Lupanov & K. A. Rybnikov, Centr Prikl. Issl. Meh.-Mat. Fak. MGU, Moscow, pp. 126–139. (Russian)


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Galochkin A.I., Nesterenko Yu.V., Chirskiy V.G., Salikhov V.I. ANDREI BORISOVICH SHIDLOVSKII. Chebyshevskii Sbornik. 2015;16(3):6-34. (In Russ.) https://doi.org/10.22405/2226-8383-2015-16-3-6-34

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