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Moscow Mathematical Journal, 2009, Volume 9, Number 3, Pages 569–623
DOI: https://doi.org/10.17323/1609-4514-2009-9-3-569-623 (Mi mmj358) 		 
This article is cited in 16 scientific papers (total in 16 papers)

Motivic Poisson summation

Ehud Hrushovski, David Kazhdan

Institute of Mathematics, the Hebrew University of Jerusalem, Jerusalem, Israel
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DOI: https://doi.org/10.17323/1609-4514-2009-9-3-569-623
Abstract: 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 show (under some assumptions) that the Fourier transform of a conjugation-invariant test function does not depend on the form of the division algebra. This yields a motivic-integration analog of certain theorems of Deligne–Kazhdan–Vigneras.
Key words and phrases: motivic integration, Poisson summation, division algebras, Grothendieck ring.
Received: October 23, 2008
Bibliographic databases:
MSC: 03C60, 11R56, 22E55
Language: English
Citation: Ehud Hrushovski, David Kazhdan, “Motivic Poisson summation”, Mosc. Math. J., 9:3 (2009), 569–623
Citation in format AMSBIB
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\by Ehud~Hrushovski, David~Kazhdan
\paper Motivic Poisson summation
\jour Mosc. Math.~J.
\yr 2009
\vol 9
\issue 3
\pages 569--623
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\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2562794}
\zmath{https://zbmath.org/?q=an:1184.03027}
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