Bulletin of the American Mathematical Society

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Book Information:

Author: Andrei B. Shidlovskii
Title: Transcendental numbers
Additional book information: Studies in mathematics, vol. 12, Walter de Gruyter, Berlin, New York, 1989, xix + 466 pp., $89.50. ISBN 3-11-011568-9.

Alan Baker, Transcendental number theory, Cambridge University Press, London-New York, 1975. MR 0422171

Frits Beukers, W. Dale Brownawell, and Gert Heckman, Siegel normality, Ann. of Math. (2) 127 (1988), no. 2, 279–308. MR 932298, DOI 10.2307/2007054

N. I. Fel′dman, Priblizheniya algebraicheskikh chisel, Moskov. Gos. Univ., Moscow, 1981 (Russian). MR 646065

N. I. Fel′dman, Sed′maya problema Gil′berta, Moskov. Gos. Univ., Moscow, 1982 (Russian). MR 710652

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

Kurt Mahler, Lectures on transcendental numbers, Lecture Notes in Mathematics, Vol. 546, Springer-Verlag, Berlin-New York, 1976. MR 0491533

David Masser, Elliptic functions and transcendence, Lecture Notes in Mathematics, Vol. 437, Springer-Verlag, Berlin-New York, 1975. MR 0379391

Wolfgang M. Schmidt, Diophantine approximation, Lecture Notes in Mathematics, vol. 785, Springer, Berlin, 1980. MR 568710

Theodor Schneider, Einführung in die transzendenten Zahlen, Springer-Verlag, Berlin-Göttingen-Heidelberg, 1957 (German). MR 0086842

11.

C. L. Siegel, Über einige Anwendungen diophantischer Approximationen, Abh. Preuss. Akad. Wiss., Phys-Math. Kl., (1929-1930), no. 1, pp. 1-70.

Carl Ludwig Siegel, Transcendental Numbers, Annals of Mathematics Studies, No. 16, Princeton University Press, Princeton, N. J., 1949. MR 0032684

Michel Waldschmidt, Nombres transcendants, Lecture Notes in Mathematics, Vol. 402, Springer-Verlag, Berlin-New York, 1974 (French). MR 0360483

Michel Waldschmidt, Transcendence methods, Queen’s Papers in Pure and Applied Mathematics, vol. 52, Queen’s University, Kingston, Ont., 1979. MR 633068

Frits Beukers, Differential Galois theory, From number theory to physics (Les Houches, 1989) Springer, Berlin, 1992, pp. 413–439. MR 1221107

Nicholas M. Katz, Exponential sums and differential equations, Annals of Mathematics Studies, vol. 124, Princeton University Press, Princeton, NJ, 1990. MR 1081536, DOI 10.1515/9781400882434

1.

A. Baker, Transcendental number theory, Cambridge Univ. Press, London, 1975. MR 0422171

2.

F. Beukers, W. D. Brownawell, and G. Heckman, Siegel normality, Ann. of Math. (2) 127 (1988), 279-308. MR 932298

3.

N. I. Feldman, Approximations of algebraic numbers, Moskov. Gos. Univ. Moscow, 1981. (Russian) MR 646065

4.

N. I. Feldman, Hilbert's Seventh Problem, Moskov. Gos. Univ., Moscow, 1982. (Russian) MR 710652

5.

A. O. Gelfond, Transcendental and algebraic numbers, Dover Publ., NY, 1960. MR 111736

6.

S. Lang, Introduction to transcendental numbers, Addison-Wesley, Reading, MA, 1966. MR 214547

7.

K. Mahler, Lectures on transcendental numbers, Lecture Notes in Math., vol. 546, Springer-Verlag, Berlin, 1976. MR 491533

8.

D. Masser, Elliptic functions and transcendence, Lecture Notes in Math., vol. 437, Springer-Verlag, Berlin, 1975. MR 379391

9.

W. M. Schmidt, Diophantine approximation, Lecture Notes in Math., vol. 785, Springer-Verlag, Berlin, 1980. MR 568710

10.

Th. Schneider, Einführung in die transzendenten Zahlen, Grundlehren Math. Wiss., vol. 81, Springer-Verlag, Berlin, 1957. MR 86842

11.

C. L. Siegel, Über einige Anwendungen diophantischer Approximationen, Abh. Preuss. Akad. Wiss., Phys-Math. Kl., (1929-1930), no. 1, pp. 1-70.

12.

C. L. Siegel, Transcendental numbers, Ann. Math. Studies, no. 16, Princeton Univ. Press, Princeton, NJ, 1949. MR 32684

13.

M. Waldschmidt, Nombres transcendants, Lecture Notes in Math., vol. 402, Springer-Verlag, Berlin, 1974. MR 360483

14.

M. Waldschmidt, Transcendence methods, Queen's Papers in Pure and Applied Math., no. 52, Queen's Univ., Kingston, Ont., 1979. MR 633068

15.

F. Beukers, Differential Galois theory, Number Theory and Physics, Proceedings Conf. Les Houches in 1989, vol. 2, Springer-Verlag, Berlin and New York, 1991 (to appear). MR 1221107

16.

N. M. Katz, Exponential sums and differential equations, Ann. Math. Studies, no. 124, Princeton Univ. Press, Princeton, NJ, 1990. MR 1081536