331 citations
- Département de mathématiques et applicationsFR20 papers
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4 papers · 1 filter
Analytic cell decomposition and analytic motivic integration
R. Cluckers, L. Lipshitz, Z. Robinson
The main results of this paper are a Cell Decomposition Theorem for Henselian valued fields with analytic structure in an analytic Denef-Pas language, and its application to analyt…
From Klein to Painleve via Fourier, Laplace and Jimbo
Philip Boalch
We will describe a method for constructing explicit algebraic solutions to the sixth Painleve equation, generalising that of Dubrovin-Mazzocco. There are basically two steps: First…
Rationalite des series de Poincare et des fonctions Zeta motiviques
Julien Sebag
If k is a field of characteristic 0, we prove that the motivic Poincare serie and the motivic Zeta functions associated to a k[[t]]-variety, flat and purely dimensional, are ration…
Motivic integration and the Grothendieck group of pseudo-finite fields
J. Denef, F. Loeser
We survey our recent work on an extension of the theory of motivic integration, called arithmetic motivic integration. We developed this theory to understand how p-adic integrals o…