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

  • * Corresponding author: Seonhee Lim

    * Corresponding author: Seonhee Lim

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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  • 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 Cα.

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


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