Publications of Vladimir Gennadievich Sprindzuk

  1. Classical Diophantine equations. Translated from the 1982 Russian original. Translation edited by Ross Talent and Alf van der Poorten. With a foreword by van der Poorten. Lecture Notes in Mathematics, 1559. Springer-Verlag, Berlin, 1993. xii+228 pp. ISBN: 3-540-57359-3
  2. Arithmetic specializations theory. New advances in transcendence theory (Durham, 1986), 366-374, Cambridge Univ. Press, Cambridge, 1988.
  3. Arithmetic specializations in polynomials. J. Reine Angew. Math. 340 (1983), 26-52.
  4. Reducibility of polynomials and rational points on algebraic curves. Seminar on Number Theory, Paris 1979-80, pp. 287-309, Progr. Math., 12, Birkhäuser, Boston, Mass., 1981
  5. Reducibility of polynomials and rational points on algebraic curves. (Russian) Dokl. Akad. Nauk SSSR 250 (1980), no. 6, 1327-1330.
  6. Achievements and problems of the theory of Diophantine approximations. (Russian) Uspekhi Mat. Nauk 35 (1980), no. 4(214), 3-68, 248.
  7. Hilbert's irreducibility theorem and rational points on algebraic curves. (Russian) Dokl. Akad. Nauk SSSR 247 (1979), no. 2, 285-289.
  8. Metric theory of Diophantine approximations. Translated from the Russian and edited by Richard A. Silverman. With a foreword by Donald J. Newman. Scripta Series in Mathematics. V. H. Winston & Sons, Washington, D.C.; A Halsted Press Book, John Wiley & Sons, New York-Toronto, Ont.-London, 1979. xiii+156 pp. ISBN: 0-470-26706-2
  9. ···, V.T. Vilcinzki, Diophantine approximations on random varieties. (Russian) Dokl. Akad. Nauk BSSR 22 (1978), no. 12, 1065-1066, 1147.
  10. Metricheskaya teoriya diofantovykh priblizhenii. (Russian) [Metric theory of Diophantine approximations] Izdat. ``Nauka'', Moscow, 1977. 143 pp.
  11. S.V. Kotov, V. Sprindzuk, The Thue-Mahler equation in a relative field, and the approximation of algebraic numbers by algebraic numbers. (Russian) Izv. Akad. Nauk SSSR Ser. Mat. 41 (1977), no. 4, 723-751, 959.
  12. The arithmetic structure of integer polynomials and class numbers. (Russian) Analytic number theory, mathematical analysis and their applications (dedicated to I. M. Vinogradov on his 85th birthday). Trudy Mat. Inst. Steklov. 143 (1977), 152-174, 210.
  13. S.V. Kotov, V. Sprindzuk, Rational approximations to algebraic numbers. (Russian) Theoretical and applied questions of algebra and differential equations (Russian), pp. 99-100, 122. Inst. Mat., Akad. Nauk Ukrain. SSR, Kiev, 1976.
  14. On extended Riemann hypothesis. Topics in number theory (Proc. Colloq., Debrecen, 1974), pp. 369-372. Colloq. Math. Soc. Janos Bolyai, Vol. 13, North-Holland, Amsterdam, 1976.
  15. V. Sprindzuk, S.V. Kotov, The approximation of algebraic numbers by algebraic numbers of a given field. (Russian) Dokl. Akad. Nauk BSSR 20 (1976), no. 7, 581-584, 667.
  16. A hyperelliptic Diophantine equation, and class numbers. (Russian) Acta Arith. 30 (1976/77), no. 1, 95-108.
  17. Diophantine equations, and class numbers of ideals. (Russian) Presented at the All-Union Conference on Number Theory (Vilnius, 1974). Mat. Zametki 17 (1975), 161-168.
  18. Proceedings of the International Conference on Number Theory (Moscow, September 14-18, 1971). With an introductory address by M. V. Keldysh, translated by B. Silver. Edited by I. M. Vinogradov, A. A. Karacuba, K. T. Oskolkov and A. N. Parshin. Cover-to-cover translation from the Russian original of Trudy Mat. Inst. Steklov. 132 (1973). Proceedings of the Steklov Institute of Mathematics, No. 132 (1973).
  19. The vertical distribution of zeros of the zeta-function and the extended Riemann hypothesis. (Russian) Collection of articles in memory of Yuri Vladimirovich Linnik. Acta Arith. 27 (1975), 317-332.
  20. An effective analysis of the Thue and Thue-Mahler equations. (Russian) Current problems of analytic number theory (Proc. Summer School, Minsk, 1972) (Russian), pp. 199-222, 272. Izdat. "Nauka i Tehnika", Minsk, 1974.
  21. Algebraic number fields with large class number. (Russian) Izv. Akad. Nauk SSSR Ser. Mat. 38 (1974), 971-982.
  22. Representation of numbers by the norm forms with two dominating variables. Collection of articles dedicated to K. Mahler on the occasion of his seventieth birthday. J. Number Theory 6 (1974), 481-486.
  23. Collection of articles. II: Dedicated to Academician I. M. Vinogradov on the eightieth anniversary of his birth. Edited by N. N. Bogoljubov, M. A. Lavrentriev, S. M. Nikolskiui, A. A. Karacuba, V. P. Mihauilov and Ju. A. Rozanov. Proceedings of the Steklov Institute of Mathematics, No. 128 (1972). Cover-to-cover translation from the Russian. American Mathematical Society, Providence, R.I., 1974. iv+303 pp.
  24. The metric theory of Diophantine approximations. (Russian) Current problems of analytic number theory (Proc. Summer School, Minsk, 1972) (Russian), pp. 178-198, 272. Izdat. "Nauka i Tehnika", Minsk, 1974.
  25. Aktualnye problemy analiticheskoui teorii chisel. (Russian) [Current problems of analytic number theory] Proceedings of the Summer School in Analytic Number Theory, Minsk, 12-21 June 1972. Edited by V. G. Sprind\v zuk. Izdat. "Nauka i Tehnika", Minsk, 1974. 272 pp.
  26. V.G. Sprindzuk, S.V. Kotov, An effective analysis of the Thue-Mahler equation in relative fields. (Russian) Dokl. Akad. Nauk BSSR 17 (1973), 393-395, 477.
  27. "Almost every" algebraic number-field has a large class-number. Acta Arith. 25 (1973/74), 411-413.
  28. The distribution of the fundamental units of real quadratic fields. Acta Arith. 25 (1973/74), 405-409.
  29. The structure of numbers representable by binary forms. (Russian) Dokl. Akad. Nauk BSSR 17 (1973), 685-688, 775.
  30. Applications of the method of trigonometric sums in the metric theory of Diophantine approximations of dependent quantities. (Russian) Proceedings of the International Conference on Number Theory (Moscow, 1971). Trudy Mat. Inst. Steklov. 132 (1973), 137-142, 265.
  31. Square-free divisors of polynomials, and class numbers of algebraic number fields. (Russian) Collection of articles dedicated to Carl Ludwig Siegel on the occasion of his seventy-fifth birthday, II. Acta Arith. 24 (1973), 143-149.
  32. Eine diophantische Eigenschaft der Trajektorien der Brownschen Bewegung. (German) Wiss. Z. Friedrich-Schiller-Univ. Jena 21 (1972), no. 1, 157-160.
  33. The method of trigonometric sums in the metric theory of Diophantine approximations of dependent variables. (Russian) Collection of articles dedicated to Academician Ivan Matveevich Vinogradov on his eightieth birthday, II. Trudy Mat. Inst. Steklov. 128 (1972), 212-228, 261.
  34. Estimation of the solutions of the Thue equation. (Russian) Izv. Akad. Nauk SSSR Ser. Mat. 36 (1972), 712-741.
  35. New applications of analytic and \$p\$-adic methods in Diophantine approximations. Actes du Congrès International des Mathématiciens (Nice, 1970), Tome 1, pp. 505-509. Gauthier-Villars, Paris, 1971.
  36. An application of the \$p\$-adic analysis in the Diophantine equations. Zahlentheorie (Tagung, Math. Forschungsinst., Oberwolfach, 1970), pp. 185-188. Ber. Math. Forschungsinst., Oberwolfach, No. 5. Bibliographisches Inst., Mannheim, 1971.
  37. The rational approximations to algebraic numbers. (Russian) Izv. Akad. Nauk SSSR Ser. Mat. 35 (1971), 991-1007.
  38. Improving the estimate of rational approximations to algebraic numbers. (Russian) Dokl. Akad. Nauk BSSR 15 (1971), 101-104.
  39. Estimates of the units of algebraic number fields. (Russian) Dokl. Akad. Nauk BSSR 15 (1971), 1065-1068.
  40. The greatest prime divisor of a binary form. (Russian) Dokl. Akad. Nauk BSSR 15 (1971) 389-391.
  41. An effective estimate of rational approximations for algebraic numbers. (Russian) Dokl. Akad. Nauk BSSR 14 (1970) 681-684.
  42. A new application of p-adic analysis to representations of numbers by binary forms. (Russian) Izv. Akad. Nauk SSSR Ser. Mat. 34 (1970) 1038-1063.
  43. On the theory of Siegel's hypergeometric functions. (Russian) Dokl. Akad. Nauk BSSR 13 (1969) 389-391.
  44. Effective estimates in "ternary" exponential diophantine equations. (Russian) Dokl. Akad. Nauk BSSR 13 (1969) 777-780.
  45. Gauss's error law in the distribution of the values of "short" Weyl sums. (Russian) Dokl. Akad. Nauk BSSR 13 (1969) 873-875.
  46. On the metric theory of "nonlinear" diophantine approximations. (Russian) Dokl. Akad. Nauk BSSR 13 (1969) 298-301.
  47. Mahler's problem in metric number theory. Translated from the Russian by B. Volkmann. Translations of Mathematical Monographs, Vol. 25 American Mathematical Society, Providence, R.I. (1969) vii+192 pp.
  48. Estimates of linear forms with \$p\$-adic logarithms of algebraic numbers. (Russian) Vesci Akad. Navuk BSSR Ser. Fiz.-Mat. Navuk (1968) no. 4, 5-14.
  49. Effectivization in certain problems of Diophantine approximation theory. (Russian) Dokl. Akad. Nauk BSSR 12 (1968) 293-297.
  50. A.I. Vinogradov, V.G. Sprindzuk, The representation of numbers by binary forms. (Russian) Mat. Zametki 3 (1968) 369-376.
  51. Quasiperiodic functions with unbounded indefinite integral. (Russian) Dokl. Akad. Nauk BSSR 12 (1968) 5-9.
  52. Irrationality of the values of certain transcendental functions. (Russian) Izv. Akad. Nauk SSSR Ser. Mat. 32 (1968) 93-107.
  53. Problema Malera v metricheskoi teorii chisel. (Russian) [Mahler's problem in metric number theory] Izdat. "Nauka i Tehnika", Minsk (1967) 181 pp.
  54. The finiteness of the number of rational and algebraic points on certain transcendental curves. (Russian) Dokl. Akad. Nauk SSSR 177 (1967) 524-527.
  55. On the metric theory of linear Diophantine approximations. (Russian) Dokl. Akad. Nauk SSSR 176 (1967) 43-45.
  56. Concerning Baker's theorem on linear forms in logarithms. (Russian) Dokl. Akad. Nauk BSSR 11 (1967) 767-769.
  57. Asymptotic behavior of the number of solutions of certain Diophantine inequalities. (Russian) Dokl. Akad. Nauk SSSR 173 (1967) 770-772.
  58. Asymptotic behavior of integrals of quasiperiodic functions. (Russian) Differencialnye Uravneniya 3 (1967) 862-868.
  59. A metric theorem on the smallest integral polynomials of several variables. (Russian) Dokl. Akad. Nauk BSSR 11 (1967) 5-6.
  60. A proof of Mahler's conjecture on the measure of the set of S-numbers. (Russian) Izv. Akad. Nauk SSSR Ser. Mat. 29 (1965) 379-436.
  61. More on Mahler's conjecture. (Russian) Dokl. Akad. Nauk SSSR 155 (1964) 54-56.
  62. On Mahler's conjecture. (Russian) Dokl. Akad. Nauk SSSR 154 (1964) 783-786.
  63. On Dilworth's theorem on partially ordered sets. (Russian) Dokl. Akad. Nauk BSSR 7 (1963) 803-804.
  64. On the measure of the set of S-numbers in a p-adic field. (Russian) Dokl. Akad. Nauk SSSR 151 (1963) 1292.
  65. On algebraic approximations in the field of power series. (Russian) Vestnik Leningrad. Univ. Ser. Mat. Meh. Astronom. 18 (1963) no. 3, 130-134.
  66. On the number of solutions of the Diophantine equation x3=y2+A. (Russian) Dokl. Akad. Nauk BSSR 7 (1963) 9-11.
  67. On a conjecture of K. Mahler concerning the measure of the set of \$S\$-numbers. (Russian) Litovsk. Mat. Sb. 2 (1962) no. 2, 221-226.
  68. Metric theorems on algebraic approximation in the field of power series. (Russian) Litovsk. Mat. Sb. 2 (1962) no. 2, 207-213.
  69. On theorems of Khinchin and Kubilius. (Russian) Litovsk. Mat. Sb. 2 (1962) no. 1, 147-152.
  70. On some general problems of approximating numbers by algebraic numbers. (Russian) Litovsk. Mat. Sb. 2 (1962) no. 1, 129-145.
  71. On a classification of transcendental numbers. (Russian) Litovsk. Mat. Sb. 2 (1962) no. 2, 215-219.
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