Explicit asymptotic expansions in $p$-adic harmonic analysis II
Abstract
Abstract We unwind the induction implicit in the “one-step” asymptotic expansions of (the author 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.
Fields of Study & Subjects
Advanced Algebra and Geometry
Algebraic Geometry and Number Theory
Geometry and complex manifolds
Publication details
- Journal / source
- Inventiones mathematicae
- Publisher
- Springer Science and Business Media LLC
- Volume
- 244
- Issue
- 3
- Pages
- 1147–1249
- Publication date
- 23 March 2026
- Language
- EN