Uniform analysis on local fields and applications to orbital integrals
Abstract
We study upper bounds, approximations, and limits for functions of motivic exponential class, uniformly in nonArchimedean local fields whose characteristic is $0$ or sufficiently large. Our results together form a flexible framework for doing analysis over local fields in a fieldindependent 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.
 Publication:

arXiv eprints
 Pub Date:
 March 2017
 arXiv:
 arXiv:1703.03381
 Bibcode:
 2017arXiv170303381C
 Keywords:

 Mathematics  Algebraic Geometry;
 Mathematics  Logic;
 Mathematics  Number Theory;
 Mathematics  Representation Theory;
 14E18 (primary);
 22E50;
 40J99
 EPrint:
 50 pages