Explicit asymptotic expansions in p-adic harmonic analysis II
Representation Theory
2026-02-03 v4
Abstract
We unwind the induction implicit in the "one-step" asymptotic expansions of arXiv:1701.02417 to describe how to turn asymptotic expansions, such as (but not limited to) the Harish-Chandra--Howe local character expansion, for depth-(0) supercuspidal characters into Kim--Murnaghan-type asymptotic expansions for arbitrary positive-depth, tame, supercuspidal characters. Doing so requires analogous results for Fourier transforms of orbital integrals on the Lie algebra of a reductive group, which are of independent interest.
Keywords
Cite
@article{arxiv.2108.12935,
title = {Explicit asymptotic expansions in p-adic harmonic analysis II},
author = {Loren Spice},
journal= {arXiv preprint arXiv:2108.12935},
year = {2026}
}
Comments
97 pages; Section 3 updated to reflect the issue in [34] discussed in [38]