Local integrability results in harmonic analysis on reductive groups in large positive characteristic

@article{Cluckers2011LocalIR,
  title={Local integrability results in harmonic analysis on reductive groups in large positive characteristic},
  author={Raf Cluckers and Julia Gordon and Immanuel Halupczok},
  journal={arXiv: Representation Theory},
  year={2011}
}
Let $G$ be a connected reductive algebraic group over a non-Archimedean local field $K$, and let $g$ be its Lie algebra. By a theorem of Harish-Chandra, if $K$ has characteristic zero, the Fourier transforms of orbital integrals are represented on the set of regular elements in $g(K)$ by locally constant functions, which, extended by zero to all of $g(K)$, are locally integrable. In this paper, we prove that these functions are in fact specializations of constructible motivic exponential… 
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