Motivic Poisson summation

Details Motivic Poisson summation Motivic Poisson summation

2009-02-05

arxiv.org/abs/0902.0845v1

Mathematics

Logic

46pp

Scientific paper

We develop a "motivic integration" version of the Poisson summation formula for function fields, with values in the Grothendieck ring of definable exponential sums. We also study division algebras over the function field, and obtain relations among the motivic Fourier transforms of a test function at different completions. We use these to prove, in a special case, a motivic version of a theorem of Deligne-Kazhdan-Vigneras.

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