Transcendental numbers. With a foreword by W. Dale Brownawell. Transl. from the Russian by Neal Koblitz. (English) Zbl 0689.10043

Shidlovskii, A. B.

De Gruyter Studies in Mathematics, 12. Berlin etc.: Walter de Gruyter. xix, 466 p. $ 77.00; DM 168.00, $ 89.00 (1989).

This English translation of A. B. Shidlovskii’s book on “Transcendental Numbers” is essentially identical in content with the Russian original published in 1987 and reviewed by K. Väänänen in Zbl 0629.10026. Some misprints and inaccuracies have been removed, and some interesting new contributions made since the publication of the original version are summarized in an appendix (of 8 pages) at the end of the book. Also the original bibliography is completed by 25 items which appeared between 1983 and 1988.
Last but not least W. D. Brownawell’s foreword to the English translation should be mentioned where the reader will find some illuminating comments on the very last development as well as five of the outstanding complexes of open problems in the topic covered by this book.

Reviewer: Peter Bundschuh (Köln)

MSC:

11J81

Transcendence (general theory)

Keywords:

arithmetic properties of E-functions; measures of transcendence; algebraic independence; values of E-functions at algebraic points; linear differential equations; Kummer functions; Bessel functions; quantitative results; IE-functions; KE-function; Siegel’s method

Citations:

Zbl 0629.10026