Sciweavers

Share
FFA
2011

Exponential sums and polynomial congruences along p-adic submanifolds

7 years 8 months ago
Exponential sums and polynomial congruences along p-adic submanifolds
In this article, we consider the estimation of exponential sums along the points of the reduction mod pm of a p-adic analytic submanifold of Zn p . More precisely, we extend Igusa’s stationary phase method to this type of exponential sums. We also study the number of solutions of a polynomial congruence along the points of the reduction mod pm of a p-adic analytic submanifold of Zn p . In addition, we attach a Poincaré series to these numbers, and establish its rationality. In this way, we obtain geometric bounds for the number of solutions of the corresponding polynomial congruences.
Dirk Segers, W. A. Zuniga-Galindo
Added 28 Aug 2011
Updated 28 Aug 2011
Type Journal
Year 2011
Where FFA
Authors Dirk Segers, W. A. Zuniga-Galindo
Comments (0)
books