Submission date: 15 March 2019

Abstract:

Doctoral thesis, University of Lille

This thesis contains some new results on the uniform rationality of Poincaré series of p-adic equivalence relations and Igusa's conjecture on exponential sums.

Mathematics Subject Classification: 11L07, 03C98, 14E18, 11L05, 11S40, 11U09, 12L12, 11F85, 11T23, 14M25, 03C60, 03C10, 11M41

Keywords and phrases:

Full text arXiv 1903.06738: pdf, ps.