Search results for "Diophantine approximation"

showing 4 items of 4 documents

The Lang–Vojta Conjectures on Projective Pseudo-Hyperbolic Varieties

2020

These notes grew out of a mini-course given from May 13th to May 17th at UQAM in Montreal during a workshop on Diophantine Approximation and Value Distribution Theory.

Pure mathematicsDistribution (number theory)Projective testDiophantine approximationAutomorphismValue (mathematics)Moduli spaceMathematics
researchProduct

Appendix: Diophantine Approximation on Hyperbolic Surfaces

2002

In this (independent) appendix, we study the Diophantine approximation properties for the particular case of the cusped hyperbolic surfaces, in the spirit of Sect. 2 (or [11]), and the many still open questions that arise for them. We refer to [9], [10]for fundamental results and further developments. We study in particular the distance to a cusp of closed geodesics on a hyperbolic surface.

Surface (mathematics)Cusp (singularity)Pure mathematicsGeodesicDiophantine setMathematics::Number TheoryDiophantine equationMathematical analysisHyperbolic manifoldDiophantine approximationMathematics::Geometric TopologyMathematicsClosed geodesic
researchProduct

On the nonarchimedean quadratic Lagrange spectra

2018

We study Diophantine approximation in completions of functions fields over finite fields, and in particular in fields of formal Laurent series over finite fields. We introduce a Lagrange spectrum for the approximation by orbits of quadratic irrationals under the modular group. We give nonarchimedean analogs of various well known results in the real case: the closedness and boundedness of the Lagrange spectrum, the existence of a Hall ray, as well as computations of various Hurwitz constants. We use geometric methods of group actions on Bruhat-Tits trees. peerReviewed

Pure mathematicscontinued fraction expansionGeneral MathematicsLaurent seriesLagrange spectrumDiophantine approximationalgebra01 natural sciences[MATH.MATH-GR]Mathematics [math]/Group Theory [math.GR]Group actionQuadratic equationModular group0103 physical sciences0101 mathematicsquadratic irrationalContinued fractionMathematicslukuteoriaMathematics - Number TheoryHall ray010102 general mathematicsSpectrum (functional analysis)ryhmäteoriapositive characteristicformal Laurent series[MATH.MATH-NT]Mathematics [math]/Number Theory [math.NT]Finite fieldHurwitz constantAMS codes: 11J06 11J70 11R11 20E08 20G25010307 mathematical physics11J06 11J70 11R11 20E08 20G25
researchProduct

A Survey of Some Arithmetic Applications of Ergodic Theory in Negative Curvature

2017

This paper is a survey of some arithmetic applications of techniques in the geometry and ergodic theory of negatively curved Riemannian manifolds, focusing on the joint works of the authors. We describe Diophantine approximation results of real numbers by quadratic irrational ones, and we discuss various results on the equidistribution in \(\mathbb{R}\), \(\mathbb{C}\) and in the Heisenberg groups of arithmetically defined points. We explain how these results are consequences of equidistribution and counting properties of common perpendiculars between locally convex subsets in negatively curved orbifolds, proven using dynamical and ergodic properties of their geodesic flows. This exposition…

ergodic theoryMathematics::Dynamical SystemsGeodesicHyperbolic geometry010102 general mathematics05 social sciencesDiophantine approximation01 natural sciencesarithmetic applicationsBianchi group0502 economics and businessHeisenberg groupBinary quadratic formErgodic theorygeometria0101 mathematicsArithmetic050203 business & managementReal numberMathematics
researchProduct