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TITLE EQUIDISTRIBUTION WITH AN ERROR RATE AND DIOPHANTINE APPROXIMATION OVER A LOCAL FIELD OF POSITIVE CHARACTERISTIC
KIAS AUTHORS Kwon, Sanghoon
JOURNAL DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2018
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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-alpha.
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