Integrability of oscillatory functions on local fields: transfer principles
Abstract
For oscillatory functions on local fields coming from motivic exponential functions, we show that integrability over $Q_p^n$ implies integrability over $F_p ((t))^n$ for large $p$, and vice versa. More generally, the integrability only depends on the isomorphism class of the residue field of the local field, once the characteristic of the residue field is large enough. This principle yields general local integrability results for HarishChandra characters in positive characteristic as we show in other work. Transfer principles for related conditions such as boundedness and local integrability are also obtained. The proofs rely on a thorough study of loci of integrability, to which we give a geometric meaning by relating them to zero loci of functions of a specific kind.
 Publication:

arXiv eprints
 Pub Date:
 November 2011
 arXiv:
 arXiv:1111.4405
 Bibcode:
 2011arXiv1111.4405C
 Keywords:

 Mathematics  Algebraic Geometry;
 Mathematics  Logic;
 Mathematics  Number Theory;
 Mathematics  Representation Theory;
 14E18 (Primary) 22E50;
 40J99 (Secondary)
 EPrint:
 44 pages