#### 55 Citations

Dyson's lemma with moving parts

- Mathematics
- 1998

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 algebraic… Expand

Uma demonstração do teorema de Thue-Siegel-Dyson-Roth

- Philosophy
- 2012

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 of… Expand

Approximating rational points on toric varieties

- Mathematics
- 2020

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 a… Expand

Local positivity and effective Diophantine approximation

- Mathematics
- 2020

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 algebraic… Expand

Generalizations of the Gap Principle and the Thue-Siegel Principle, with Applications to Diophantine Equations

- Mathematics
- 2019

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 their… Expand

Growth and integrability in multi-valued dynamics

- Mathematics
- 2018

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 cubic… Expand

Mahler's work on Diophantine equations and subsequent developments

- Mathematics
- 2018

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

- Mathematics
- 2018

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

- Mathematics
- 2017

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 helpf… Expand

Klaus Friedrich Roth. 29 October 1925 — 10 November 2015

- Computer Science
- Biographical Memoirs of Fellows of the Royal Society
- 2017

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

#### References

SHOWING 1-4 OF 4 REFERENCES

Approximation algebraischer Zahlen

- Mathematics
- 1921

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 oder… Expand