Submission date: 23 February 2015.

Abstract:

We show that the class of L-constructible functions is closed under integration for any P-minimal expansion of a p-adic field (K,L). This generalizes results previously known for semi-algebraic and sub-analytic structures. As part of the proof, we obtain a weak version of cell decomposition and function preparation for P-minimal structures, a result which is independent of the existence of Skolem functions. The result is obtained from weak versions of cell decomposition and function preparation which we prove for general P-minimal structures. A direct corollary is that Denef's results on the rationality of Poincaré series hold in any P-minimal expansion of a p-adic field (K,L).

Mathematics Subject Classification: 12J12, 03c10, 11u09. Secondary: 03c07, 03c64

Keywords and phrases:

Full text arXiv 1502.06467: pdf, ps.