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Book Review

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Book Information:

Author: Alan Baker
Title: Transcendental number theory
Additional book information: Cambridge Univ. Press, New York, 1975, x + 147 pp., $13.95.

Author: Kurt Mahler
Title: Lectures on transcendental numbers
Additional book information: Edited and completed by B. Diviš and W. J. LeVeque, Lecture Notes in Math., no. 546, Springer-Verlag, Berlin, Heidelberg, New York, 1976, xxi + 254 pp., $10.20.

Author: Michel Waldschmidt
Title: Nombres transcendants
Additional book information: Lecture Notes in Math., no. 402, Springer-Verlag, Berlin and New York, 1974, viii + 277 pp., $10.30.

References [Enhancements On Off] (What's this?)

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  • 2. A. Baker, Rational approximations to 21/3 and other algebraic numbers, Quart. J. Math. Oxford Ser. (2) 15 (1964), 375-383. MR 171750
  • 3. E. A. Bender, Asymptotic methods in enumeration, SIAM Rev. 16 (1974), 485-515. MR 376369
  • 4. P. Bundschuh, Irrationalitätsmasse für e ≠ 0 rational oder Liouville-Zahl, Math. Ann. 192 (1971), 229-242. MR 286753
  • 5. J. W. S. Cassels, An introduction to Diophantine approximation, Cambridge Univ. Press, Cambridge, London and New York, 1965. MR 87708
  • 6. C. E. Corzatt, A large algebraically closed field, Proc. Amer. Math. Soc. 46 (1974), 191-194. MR 360546
  • 7. H. Davenport, A note on Thue's theorem, Mathematika 15 (1968), 76-87. MR 230689
  • 8. H. Diamond and H. Pollard, The theory of algebraic numbers, 2nd ed., Carus Math. Monograph, no. 9, Mathematical Association of America, Wiley, New York, 1975.
  • 9. N. I. Feldman and A. B. Shidlovskiĭ, The development and the present state of the theory of transcendental numbers, Russian Math. Surveys 22 (1967), 1-79. MR 214551
  • 10. A. O. Gelfond, Transcendental and algebraic numbers, Dover, New York, 1960. MR 111736
  • 11. S. Lang, Introduction to transcendental numbers, Addison-Wesley, Reading, Mass., 1966. MR 214547
  • 12. S. Lang, Transcendental numbers and diophantine approximations, Bull. Amer. Math. Soc. 77 (1971), 635-677. MR 289424
  • 13. K. Mahler, Ein Beweis des Thue-Siegelschen Satzes über die Approximation algebraischer Zahlen für binomische Gleichungen, Math. Ann. 105 (1931), 267-276. MR 1512715
  • 14. I. Niven, Irrational numbers, Carus Math. Monograph, no. 11, Mathematical Association of America, Wiley, New York, 1956. MR 80123
  • 15. G. Pólya, Kombinatorische Anzahlbestimmungen für Gruppen, Graphen and chemische Verbindungen, Acta Math. 68 (1937), 145-254.
  • 16. K. F. Roth, Rational approximations to algebraic numbers, Mathematika 2 (1955), 1-20; Corrigendum, ibid., 168. MR 72182
  • 17. W. M. Schmidt, Approximation to algebraic numbers, Enseignement Math. 17 (1971), 188-253. MR 327672
  • 18. V. G. Sprindzuk, Mahler's problem in metric number theory, Transl. Math. Monographs, no. 25, Amer. Math. Soc., Providence, R. I., 1969. MR 245527
  • 19. P. Stäckel, Ueber arithmetische Eigenschaften analytischer Funktionen, Math. Ann. 46 (1895), 513-520.

Review Information:

Reviewer: Kenneth B. Stolarsky
Journal: Bull. Amer. Math. Soc. 84 (1978), 1370-1378
DOI: https://doi.org/10.1090/S0002-9904-1978-14584-4
American Mathematical Society