Multivariate Igusa theory: Decay rates of exponential sums

Raf Cluckers

We obtain general estimates for exponential integrals of the form \[ E_f(y)=\int_{\mathbb{Z}_{p}^{n}}ψ(\sum_{j=1}^r y_j f_j(x))|dx|, \] where the $f_j$ are restricted power series…