The approximation to algebraic numbers by rationals

  title={The approximation to algebraic numbers by rationals},
  author={F. Dyson},
  journal={Acta Mathematica},
  • F. Dyson
  • Published 1947
  • Mathematics
  • Acta Mathematica
Dyson's lemma with moving parts
In its original form [D], Dyson’s Lemma bounds the order of vanishing of a polynomial in two variables at a finite set of points and was used in studying rational approximations to a fixed algebraicExpand
Uma demonstração do teorema de Thue-Siegel-Dyson-Roth
In this work we study the celebrated Klaus F. Roth's Theorem in Diophantine approximations, also known as the Thue-Siegel-Roth Theorem. Our goals are to make a comprehensive study of the evolution ofExpand
Approximating rational points on toric varieties
Given a smooth projective variety $X$ over a number field $k$ and $P\in X(k)$, the first author conjectured that in a precise sense, any sequence that approximates $P$ sufficiently well must lie on aExpand
Local positivity and effective Diophantine approximation
In this paper we present a new approach to prove effective results in Diophantine approximation. We then use it to prove an effective theorem on the simultaneous approximation of two algebraicExpand
Generalizations of the Gap Principle and the Thue-Siegel Principle, with Applications to Diophantine Equations
In this thesis we develop generalizations of two well-known principles from the theory of Diophantine approximation, namely the gap principle and the Thue-Siegel principle. Our results find theirExpand
Growth and integrability in multi-valued dynamics
This thesis is focused on the problem of growth and integrability in multi-valued dynamics generated by $SL_2 (\mathbb{Z})$ actions. An important example is given by Markov dynamics on the cubicExpand
Mahler's work on Diophantine equations and subsequent developments
We discuss Mahler's work on Diophantine approximation and its applications to Diophantine equations, in particular Thue-Mahler equations, S-unit equations and S-integral points on elliptic curves,Expand
Roth's Theorem over arithmetic function fields
Roth's theorem is extended to finitely generated field extensions of $\Bbb Q$, using Moriwaki's framework for heights.
Generalized Vandermonde matrices and determinants in electromagnetic compatibility
Matrices whose rows (or columns) consists of monomials of sequential powers are called Vandermonde matrices and can be used to describe several useful concepts and have properties that can be helpfExpand
Klaus Friedrich Roth. 29 October 1925 — 10 November 2015
Klaus Friedrich Roth, who died in Inverness on 10 November 2015 aged 90, made fundamental contributions to different areas of number theory, including diophantine approximation, the large sieve,Expand


Approximation algebraischer Zahlen
ersetzt werden kann. Mit YIilfe hiervon bewies dann Thue seinen bekannten Satz: Bedeutet U (x, y) eine homogene biniire Form mit rationalen Koeffizienten, die nieht Potenz einer linearen oderExpand
Über Näherungswerte algebraischer Zahlen