Submission date: 15 December 2014.

Abstract:

We study transfer principles for upper bounds of motivic exponential functions and for linear combinations of such functions, directly generalizing the transfer principles from [7] by Cluckers-Loeser and [13, Appendix B] by Shin-Templier (appendix B by Cluckers-Gordon-Halupczok). These functions come from rather general oscillatory integrals on local fields, and can be used to describe e.g. Fourier transforms of orbital integrals. One of our techniques consists in reducing to simpler functions where the oscillation only comes from the residue field.

Mathematics Subject Classification: Primary 14E18, Secondary 22E50, 40J99

Keywords and phrases:

Full text arXiv 1412.4573: pdf, ps.