Equidistribution with an error rate and Diophantine approximation over a local field of positive characteristic

Sanghoon Kwon; Seonhee Lim

doi:10.3934/dcds.2018008

Article Contents

2018, Volume 38, Issue 1: 169-186. Doi: 10.3934/dcds.2018008

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Equidistribution with an error rate and Diophantine approximation over a local field of positive characteristic

Sanghoon Kwon^1, and
Seonhee Lim^2, ,

1.
Center for Mathematical Challenges, Korea Institute For Advanced Study, Seoul 02455, Korea
2.
Department of Mathematical Sciences, Seoul National University, Seoul 08826, Korea

* Corresponding author: Seonhee Lim
* Corresponding author: Seonhee Lim

Received: September 2016

Revised: July 2017

Published: October 2017

The second author is supported by Samsung Science and Technology Foundation under Project No. SSTF-BA1601-03 and is an associate member of KIAS.

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Abstract

For a local field K of formal Laurent series and its ring Z of polynomials, we prove a pointwise equidistribution with an error rate of each H-orbit in SL(d, K)/SL(d, Z) for a certain proper subgroup H of a horospherical group, extending a work of Kleinbock-Shi-Weiss.

We obtain an asymptotic formula for the number of integral solutions to the Diophantine inequalities with weights, generalizing a result of Dodson-Kristensen-Levesley. This result enables us to show pointwise equidistribution for unbounded functions of class C_α.

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Mathematics Subject Classification: Primary; 28A33;Secondary:37A15, 22E40.

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References

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