# Simon Kristensen

## Metric inhomogeneous Diophantine approximation in positive characteristic

Research output: Contribution to journal/Conference contribution in journal/Contribution to newspaperJournal articleResearchpeer-review

### Standard

In: Mathematica Scandinavica, Vol. 108, No. 1, 2011, p. 55-76.

Research output: Contribution to journal/Conference contribution in journal/Contribution to newspaperJournal articleResearchpeer-review

### Harvard

Kristensen, S 2011, 'Metric inhomogeneous Diophantine approximation in positive characteristic' Mathematica Scandinavica, vol. 108, no. 1, pp. 55-76.

### Author

Kristensen, Simon. / Metric inhomogeneous Diophantine approximation in positive characteristic. In: Mathematica Scandinavica. 2011 ; Vol. 108, No. 1. pp. 55-76

### Bibtex

@article{57ae9d994b524888b12a1126d5a9839b,
title = "Metric inhomogeneous Diophantine approximation in positive characteristic",
abstract = "We obtain asymptotic formulae for the number of solutions to systems of inhomogeneous linear Diophantine inequalities over the field of formal Laurent series with coefficients from a finite fields, which are valid for almost every such system. Here almost every' is with respect to Haar measure of the coefficients of the homogeneous part when the number of variables is at least two (singly metric case), and with respect to the Haar measure of all coefficients for any number of variables (doubly metric case). As consequences, we derive zero-one laws in the spirit of the Khintchine-Groshev Theorem and zero-infinity laws for Hausdorff measure in the spirit of Jarn{\'i}k's Theorem. The latter result depends on extending a recently developed slicing technique of Beresnevich and Velani to the present setup.",
author = "Simon Kristensen",
year = "2011",
language = "English",
volume = "108",
pages = "55--76",
journal = "Mathematica Scandinavica",
issn = "0025-5521",
publisher = "Aarhus Universitet * Mathematica Scandinavica",
number = "1",

}

### RIS

TY - JOUR

T1 - Metric inhomogeneous Diophantine approximation in positive characteristic

AU - Kristensen,Simon

PY - 2011

Y1 - 2011

N2 - We obtain asymptotic formulae for the number of solutions to systems of inhomogeneous linear Diophantine inequalities over the field of formal Laurent series with coefficients from a finite fields, which are valid for almost every such system. Here almost every' is with respect to Haar measure of the coefficients of the homogeneous part when the number of variables is at least two (singly metric case), and with respect to the Haar measure of all coefficients for any number of variables (doubly metric case). As consequences, we derive zero-one laws in the spirit of the Khintchine-Groshev Theorem and zero-infinity laws for Hausdorff measure in the spirit of Jarník's Theorem. The latter result depends on extending a recently developed slicing technique of Beresnevich and Velani to the present setup.

AB - We obtain asymptotic formulae for the number of solutions to systems of inhomogeneous linear Diophantine inequalities over the field of formal Laurent series with coefficients from a finite fields, which are valid for almost every such system. Here `almost every' is with respect to Haar measure of the coefficients of the homogeneous part when the number of variables is at least two (singly metric case), and with respect to the Haar measure of all coefficients for any number of variables (doubly metric case). As consequences, we derive zero-one laws in the spirit of the Khintchine-Groshev Theorem and zero-infinity laws for Hausdorff measure in the spirit of Jarník's Theorem. The latter result depends on extending a recently developed slicing technique of Beresnevich and Velani to the present setup.

M3 - Journal article

VL - 108

SP - 55

EP - 76

JO - Mathematica Scandinavica

T2 - Mathematica Scandinavica

JF - Mathematica Scandinavica

SN - 0025-5521

IS - 1

ER -