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Michel Waldschmidt

  1. Auxiliary functions in transcendence proofs.

    Пт, 08/28/2009 - 23:56 — SomNambul
    Authors: Michel Waldschmidt
    Subjects: Number Theory
    Abstract

    We discuss the role of auxiliary functions in the development of
    transcendental number theory.

  2. Perfect Powers: Pillai's works and their developments.

    Пт, 08/28/2009 - 23:56 — SomNambul
    Authors: Michel Waldschmidt
    Subjects: Number Theory
    Abstract

    After a short introduction to Pillai's work on Diophantine questions, we
    quote some later developments and we discuss related open problems.

  3. Words and Transcendence.

    Пт, 08/28/2009 - 23:56 — SomNambul
    Authors: Michel Waldschmidt
    Subjects: Number Theory
    Abstract

    Is it possible to distinguish algebraic from transcendental real numbers by
    considering the $b$-ary expansion in some base $b\ge2$? In 1950, \'E. Borel
    suggested that the answer is no and that for any real irrational algebraic
    number $x$ and for any base $g\ge2$, the $g$-ary expansion of $x$ should
    satisfy some of the laws that are shared by almost all numbers.

  4. Report on some recent advances in Diophantine approximation.

    Пт, 08/28/2009 - 23:56 — SomNambul
    Authors: Michel Waldschmidt
    Subjects: Number Theory
    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.

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