000			01844 a2200229 4500
008			220820b |||||||| |||| 00| 0 eng d
020			_a 9780521045674
082			_a512.74 _bBUG
100			_aBugeaud, Yann
245			_aApproximation by algebraic numbers
260			_bCambridge University Press, _c2007. _aCambridge:
300			_axv, 274p.; _bpbk; _c24cm.
440			_aCambridge tracts in mathematics, no. 160
504			_aIncludes index and references
520			_aAlgebraic numbers can approximate and classify any real number. Here, the author gathers together results about such approximations and classifications. Written for a broad audience, the book is accessible and self-contained, with complete and detailed proofs. Starting from continued fractions and Khintchine's theorem, Bugeaud introduces a variety of techniques, ranging from explicit constructions to metric number theory, including the theory of Hausdorff dimension. So armed, the reader is led to such celebrated advanced results as the proof of Mahler's conjecture on S-numbers, the Jarnik–Besicovitch theorem, and the existence of T-numbers. Brief consideration is given both to the p-adic and the formal power series cases. Thus the book can be used for graduate courses on Diophantine approximation (some 40 exercises are supplied), or as an introduction for non-experts. Specialists will appreciate the collection of over 50 open problems and the rich and comprehensive list of more than 600 references. https://www.cambridge.org/core/books/approximation-by-algebraic-numbers/6BDC86829D61A4CC2AD2463DEB4E1A6A#fndtn-information
650			_aApproximation theory
650			_aAlgebraic number theory
650			_aApproximate identities--Algebra
650			_aJarnik–Besicovitch theorem
650			_aKhintchine's theorem
942			_2ddc _cTD
999			_c56667 _d56667