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Stéphane Fischler

  1. Seshadri Constants and Interpolation on Commutative Algebraic Groups.

    Пнд, 05/21/2012 - 15:01 — SomNambul
    Authors: Stéphane Fischler, Michael Nakamaye
    Subjects: Number Theory
    Abstract

    In this article we study interpolation estimates on a special class of
    compactifications of commutative algebraic groups constructed by Serre. We
    obtain a large quantitative improvement over previous results due to Masser and
    the first author and our main result has the same level of accuracy as the best
    known multiplicity estimates. The improvements come both from using special
    properties of the compactifications which we consider and from a different
    approach based upon Seshadri constants and vanishing theorems.

  2. Nesterenko's linear independence criterion for vectors.

    Пнд, 02/13/2012 - 15:01 — SomNambul
    Authors: Stéphane Fischler
    Subjects: Number Theory
    Abstract

    In this paper we deduce a lower bound for the rank of a family of $p$ vectors
    in $\R^k$ (considered as a vector space over the rationals) from the existence
    of a sequence of linear forms on $\R^p$, with integer coefficients, which are
    small at $k$ points. This is a generalization to vectors of Nesterenko's linear
    independence criterion (which corresponds to $k=1$). It enables one to make use
    of some known constructions of linear forms small at several points, related to
    Pad\'e approximation.

  3. Irrationality exponent and rational approximations with prescribed growth.

    Пнд, 10/26/2009 - 14:10 — SomNambul
    Authors: Stéphane Fischler, Tanguy Rivoal
    Subjects: Number Theory
    Abstract

    Let $\xi$ be a real irrational number. We are interested in sequences of
    linear forms in 1 and $\xi$, with integer coefficients, which tend to 0. Does
    such a sequence exist such that the linear forms are small (with given rate of
    decrease) and the coefficients have some given rate of growth? If these rates
    are essentially geometric, a necessary condition for such a sequence to exist
    is that the linear forms are not too small, a condition which can be expressed
    precisely using the irrationality exponent of $\xi$.

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