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Book Information

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

Author(s): 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(s): 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

1.: A. Baker, Linear forms in the logarithms of algebraic numbers. I, II, Mathematika 13 (1966), 204-216; 14 (1967), 102-107. MR 258756
2.: A. Baker, Rational approximations to 2^1/3 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:
Journal: Bull. Amer. Math. Soc. 84 (1978), 1370-1378.
DOI: 10.1090/S0002-9904-1978-14584-4
PII: S 0002-9904(1978)14584-4

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ISSN 1936-881X(e) ISSN 0002-9904(p)

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