On transfer inequalities in Diophantine approximation

By Michel Laurent. 2007

52 citations recorded by the source corpus.

We refine Khintchine Transference Principle which relates the measure of simultaneous rational approximation of an $n$ real numbers with the measure of linear independence of these $n$ numbers. Khintchine's inequalities are known to be optimal. However, they may be sharpened by taking into account two further uniform exponents.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/182a131c87acc61cf960876003d43ca57f0c1631

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

1. Yann Bugeaud
2. Damien Roy
3. Samir Siksek

In Geometry and Topology

1. Yann Bugeaud
2. Damien Roy
3. Samir Siksek

In Mathematical Physics

1. Yann Bugeaud
2. Damien Roy
3. Boris Adamczewski
4. Michel Waldschmidt
5. Samir Siksek

Citations in the corpus

• On Schmidt and Summerer parametric geometry of numbers (2014, background): “Based on this, they recover the celebrated Khintchine’s and Jarńık’s transference principles [4], [5], [6] as well as more recent results of Bugeaud, Laurent and Moshchevitin from [1], [7], [8], [12].”
• Exponents of Diophantine approximation (2006, background): “We follow the proof of the Corollary from [46], where it is established that, for any λ with 1/n ≤ λ ≤ +∞ and for any point ξ in R such that ωn,0(ξ) = λ and ωn,n−1(ξ) = nλ+ n− 1, we have”