Uniform analysis on local fields and applications to orbital integrals

Autor:	Cluckers, Raf, Gordon, Julia, Halupczok, Immanuel
Rok vydání:	2017
Předmět:	Mathematics - Algebraic Geometry Mathematics - Logic Mathematics - Number Theory Mathematics - Representation Theory 14E18 (primary) 22E50 40J99
Druh dokumentu:	Working Paper
Popis:	We study upper bounds, approximations, and limits for functions of motivic exponential class, uniformly in non-Archimedean local fields whose characteristic is $0$ or sufficiently large. Our results together form a flexible framework for doing analysis over local fields in a field-independent way. As corollaries, we obtain many new transfer principles, for example, for local constancy, continuity, and existence of various kinds of limits. Moreover, we show that the Fourier transform of an $L^2$-function of motivic exponential class is again of motivic exponential class. As an application in the realm of representation theory, we prove uniform bounds for the normalized by the discriminant Fourier transforms of orbital integrals on connected reductive $p$-adic groups. Comment: 50 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1703.03381 Zobrazit plný text záznamu View this record from Arxiv