Recent advances in Diophantine approximation

Michel Waldschmidt ()
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Michel Waldschmidt: Université Pierre et Marie Curie–Paris 6, UMR 7586 IMJ Institut de, Mathématiques de Jussieu

A chapter in Number Theory, Analysis and Geometry, 2012, pp 659-704 from Springer

Abstract: Abstract A basic question of Diophantine approximation, which is the first issue we discuss, is to investigate the rational approximations to a single real number. Next, we consider the algebraic or polynomial approximations to a single complex number, as well as the simultaneous approximation of powers of a real number by rational numbers with the same denominator. Finally we study generalisations of these questions to higher dimensions. Several recent advances have been made by B. Adamczewski, Y. Bugeaud, S. Fischler, M. Laurent, T. Rivoal, D. Roy, and W.M. Schmidt, among others. We review some of these works.

Keywords: Diophantine approximation; rational approximation; simultaneous approximation; approximation by algebraic numbers; approximation by linear forms; irrationality measures; transcendence criterion; criteria for algebraic independence; Dirichlet; Hurwitz; Thue-Siegel-Roth-Schmidt; Khintchine; Davenport; Sprindzuck; Laurent; Roy (search for similar items in EconPapers)
Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4614-1260-1_29

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DOI: 10.1007/978-1-4614-1260-1_29

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