Explicit asymptotic expansions in p\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$p$\end{document}-adic harmonic analy

We unwind the induction implicit in the “one-step” asymptotic expansions of (the au- thor in Compositio Mathematica 154(11):2305–2378, 2018) 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. MathematicsSubjectClassification 22E50· 22E35 Contents