Year: 2016
Type: preprint
Abstract: We prove pointwise equidistribution with an error rate of each $H$-orbit in $SL(d,\mathbf{K})/SL(d,\mathbf{Z})$ for a certain proper subgroup $H$ of horospherical group over a function field $\mathbf{K}$, extending a work of Kleinbock-Shi-Weiss. Moreover, 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 $C_α$, which was first introduced by Eskin-Margulis-Mozes.
Source: arXiv (Cornell University)
Authors: Kwon, Sanghoon, Lim, Seonhee
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Award: G2741380458
OpenAlex ID: W2507126320