Bulletin of the American Mathematical Society

MathSciNet review: 1567103
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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.

A. Baker, Linear forms in the logarithms of algebraic numbers. IV, Mathematika 15 (1968), 204–216. MR 258756, DOI 10.1112/S0025579300002588

A. Baker, Rational approximations to $\root 3\of 2$ and other algebraic numbers, Quart. J. Math. Oxford Ser. (2) 15 (1964), 375–383. MR 171750, DOI 10.1093/qmath/15.1.375

Edward A. Bender, Asymptotic methods in enumeration, SIAM Rev. 16 (1974), 485–515. MR 376369, DOI 10.1137/1016082

Peter Bundschuh, Irrationalitätsmaße für $e^{a},\,a\not =0$ rational oder Liouville-Zahl, Math. Ann. 192 (1971), 229–242 (German). MR 286753, DOI 10.1007/BF02052875

J. W. S. Cassels, An introduction to Diophantine approximation, Cambridge Tracts in Mathematics and Mathematical Physics, No. 45, Cambridge University Press, New York, 1957. MR 0087708

Clifton E. Corzatt, A large algebraically closed field, Proc. Amer. Math. Soc. 46 (1974), 191–194. MR 360546, DOI 10.1090/S0002-9939-1974-0360546-6

H. Davenport, A note on Thue’s theorem, Mathematika 15 (1968), 76–87. MR 230689, DOI 10.1112/S0025579300002412

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.

N. I. Fel′dman and A. B. Šidlovskiĭ, The development and present state of the theory of transcendental numbers, Uspehi Mat. Nauk 22 (1967), no. 3 (135), 3–81 (Russian). MR 0214551

A. O. Gel′fond, Transcendental and algebraic numbers, Dover Publications, Inc., New York, 1960. Translated from the first Russian edition by Leo F. Boron. MR 0111736

Serge Lang, Introduction to transcendental numbers, Addison-Wesley Publishing Co., Reading, Mass.-London-Don Mills, Ont., 1966. MR 0214547

Serge Lang, Transcendental numbers and diophantine approximations, Bull. Amer. Math. Soc. 77 (1971), 635–677. MR 289424, DOI 10.1090/S0002-9904-1971-12761-1

Kurt Mahler, Ein Beweis des Thue-Siegelschen Satzes über die Approximation algebraischer Zahlen für binomische Gleichungen, Math. Ann. 105 (1931), no. 1, 267–276 (German). MR 1512715, DOI 10.1007/BF01455819

Ivan Niven, Irrational numbers, The Carus Mathematical Monographs, No. 11, Mathematical Association of America; distributed by John Wiley & Sons, Inc., New York, N.Y., 1956. MR 0080123

15.

G. Pólya, Kombinatorische Anzahlbestimmungen für Gruppen, Graphen and chemische Verbindungen, Acta Math. 68 (1937), 145-254.

K. F. Roth, Rational approximations to algebraic numbers, Mathematika 2 (1955), 1–20; corrigendum, 168. MR 72182, DOI 10.1112/S0025579300000644

Wolfgang M. Schmidt, Approximation to algebraic numbers, Enseign. Math. (2) 17 (1971), 187–253. MR 327672

V. G. Sprindžuk, Mahler’s problem in metric number theory, Translations of Mathematical Monographs, Vol. 25, American Mathematical Society, Providence, R.I., 1969. Translated from the Russian by B. Volkmann. MR 0245527

19.

P. Stäckel, Ueber arithmetische Eigenschaften analytischer Funktionen, Math. Ann. 46 (1895), 513-520.

1.

A. Baker, Linear forms in the logarithms of algebraic numbers. I, II, Mathematika 13 (1966), 204-216; 14 (1967), 102-107. MR 0258756

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.