A quantitative Khintchine-Groshev type theorem over a field of formal series

J. Levesley; Maurice Dodson; Simon Kristensen

doi:10.1016/S0019-3577(05)80020-5

A quantitative Khintchine-Groshev type theorem over a field of formal series

J. Levesley, Maurice Dodson, Simon Kristensen

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

An asymptotic formula which holds almost everywhere is obtained for the number of solutions to theDiophantine inequalities double vertical barqA - pdouble vertical bar <¿(double vertical bargdouble vertical bar), where A is an n x m matrix (m > 1) over the field of formal Laurent series with coefficients from a finite field, and p and q are vectors of polynomials over the same finite field.

Original language	English
Pages (from-to)	171-177
Number of pages	6
Journal	Indagationes Mathematicae
Volume	16
Issue number	2
DOIs	https://doi.org/10.1016/S0019-3577(05)80020-5
Publication status	Published - 20 Jun 2005

Keywords

Diophantine approximation,
Positive characteristic,
Systems of linear forms,
Asymptotic formulae

Access to Document

10.1016/S0019-3577(05)80020-5

http://dx.doi.org/10.1016/S0019-3577(05)80020-5

Cite this

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abstract = "An asymptotic formula which holds almost everywhere is obtained for the number of solutions to theDiophantine inequalities double vertical barqA - pdouble vertical bar <¿(double vertical bargdouble vertical bar), where A is an n x m matrix (m > 1) over the field of formal Laurent series with coefficients from a finite field, and p and q are vectors of polynomials over the same finite field.",

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AU - Dodson, Maurice

AU - Kristensen, Simon

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N2 - An asymptotic formula which holds almost everywhere is obtained for the number of solutions to theDiophantine inequalities double vertical barqA - pdouble vertical bar <¿(double vertical bargdouble vertical bar), where A is an n x m matrix (m > 1) over the field of formal Laurent series with coefficients from a finite field, and p and q are vectors of polynomials over the same finite field.

AB - An asymptotic formula which holds almost everywhere is obtained for the number of solutions to theDiophantine inequalities double vertical barqA - pdouble vertical bar <¿(double vertical bargdouble vertical bar), where A is an n x m matrix (m > 1) over the field of formal Laurent series with coefficients from a finite field, and p and q are vectors of polynomials over the same finite field.

KW - Diophantine approximation,

KW - Positive characteristic,

KW - Systems of linear forms,

KW - Asymptotic formulae

U2 - 10.1016/S0019-3577(05)80020-5

DO - 10.1016/S0019-3577(05)80020-5

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