Cluckers, R, Gordon, J and Halupczok, I (2014) Integrability of oscillatory functions on local fields: Transfer principles. Duke Mathematical Journal, 163 (8). 8. pp. 1549-1600. ISSN 0012-7094
Abstract
For oscillatory functions on local fields coming from motivic exponential functions, we show that integrability over Q n p 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 Harish-Chandra 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.
Metadata
Item Type: | Article |
---|---|
Authors/Creators: |
|
Copyright, Publisher and Additional Information: | © 2014, Duke University Press. This is an author produced version of a paper published in Duke Mathematical Journal. Uploaded in accordance with the publisher's self-archiving policy. |
Dates: |
|
Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 27 Feb 2015 15:43 |
Last Modified: | 28 Jan 2021 12:29 |
Published Version: | http://dx.doi.org/10.1215/00127094-2713482 |
Status: | Published |
Publisher: | Duke University Press |
Identification Number: | 10.1215/00127094-2713482 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:83362 |