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Asymptotic Behavior of the Number of Solutions for Non-Archimedean Diophantine Approximations with Restricted Denominators

Valerie Berthe 1 Hitoshi Nakada 2 Rie Natsui 3
1 ARITH - Arithmétique informatique
LIRMM - Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier
2 Department of Mathematics
3 Department of Mathematics
Abstract : We consider metric results for the asymptotic behavior of the number of solutions of Diophantine approximation inequalities with restricted denominators for Laurent formal power series with coefficients in a finite field. We consider, in particular, approximations by rational functions whose denominators are powers of irreducible polynomials, and we study the strong law of large numbers for solutions of the inequalities under consideration
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https://hal-lirmm.ccsd.cnrs.fr/lirmm-00344945
Contributor : Valerie Berthe <>
Submitted on : Sunday, December 7, 2008 - 12:36:46 PM
Last modification on : Monday, March 4, 2019 - 2:22:27 PM

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  • HAL Id : lirmm-00344945, version 1

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CNRS | INSMI | ARITH | LIRMM | MIPS | UNIV-MONTPELLIER

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Valerie Berthe, Hitoshi Nakada, Rie Natsui. Asymptotic Behavior of the Number of Solutions for Non-Archimedean Diophantine Approximations with Restricted Denominators. Finite Fields and Their Applications, Elsevier, 2008, 14, pp.849-866. ⟨lirmm-00344945⟩

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