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Approximation by Algebraic Numbers.


Approximation by algebraic numbers.

Bugeaud, Yann.

Cambridge U. Pr.


274 pages



Cambridge tracts in mathematics; 160


Bugeaud (Universite Louis Pasteur) surveys recent results on algebraic approximations and classifications. Starting from continued fractions and Khintchine's theorem, he introduces a variety of techniques, ranging from explicit constructions to metric number theory. The reader is led to advanced results such as the proof of Mahler's conjecture on S-numbers. Brief consideration is given to the p-adic and the formal power series cases. Some 40 exercises are included. The book can be used for a graduate course on Diophantine approximation, or as an introduction for non-experts. Specialists will appreciate the collection of 50 open problems.

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Publication:SciTech Book News
Article Type:Book Review
Date:Dec 1, 2005
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