6533b832fe1ef96bd129ae3f
RESEARCH PRODUCT
On the nonarchimedean quadratic Lagrange spectra
Jouni ParkkonenFrédéric Paulinsubject
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 20G25description
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
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2018-01-30 |