Report on some recent advances in Diophantine approximation
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.
Cite
@article{arxiv.0908.3973,
title = {Report on some recent advances in Diophantine approximation},
author = {Michel Waldschmidt},
journal= {arXiv preprint arXiv:0908.3973},
year = {2009}
}
Comments
to be published by Springer Verlag, Special volume in honor of Serge Lang, ed. Dorian Goldfeld, Jay Jorgensen, Dinakar Ramakrishnan, Ken Ribet and John Tate