Duke Mathematical Journal

Integrability of oscillatory functions on local fields: Transfer principles

Raf Cluckers, Julia Gordon, and Immanuel Halupczok

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For oscillatory functions on local fields coming from motivic exponential functions, we show that integrability over Qpn implies integrability over Fp((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.

Article information

Duke Math. J., Volume 163, Number 8 (2014), 1549-1600.

First available in Project Euclid: 26 May 2014

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Zentralblatt MATH identifier

Primary: 14E18: Arcs and motivic integration
Secondary: 22E50: Representations of Lie and linear algebraic groups over local fields [See also 20G05] 40J99: None of the above, but in this section


Cluckers, Raf; Gordon, Julia; Halupczok, Immanuel. Integrability of oscillatory functions on local fields: Transfer principles. Duke Math. J. 163 (2014), no. 8, 1549--1600. doi:10.1215/00127094-2713482. https://projecteuclid.org/euclid.dmj/1401146372

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