Local Zeta Functions for Non-degenerate Laurent Polynomials Over p-adic Fields
Abstract
In this article, we study local zeta functions attached to Laurent polynomials over p-adic fields, which are non-degenerate with respect to their Newton polytopes at infinity. As an application we obtain asymptotic expansions for p-adic oscillatory integrals attached to Laurent polynomials. We show the existence of two different asymptotic expansions for p-adic oscillatory integrals, one when the absolute value of the parameter approaches infinity, the other when the absolute value of the parameter approaches zero. These two asymptotic expansions are controlled by the poles of twisted local zeta functions of Igusa type.
Cite
@article{arxiv.1009.3680,
title = {Local Zeta Functions for Non-degenerate Laurent Polynomials Over p-adic Fields},
author = {E. Leon-Cardenal and W. A. Zuniga-Galindo},
journal= {arXiv preprint arXiv:1009.3680},
year = {2015}
}
Comments
The condition on the critical set on the mapping f considered in Section 2.5 of our article is not sufficient to assure the vanishing of the twisted local zeta functions (for almost all the characters) as we assert in Theorem 3.9. A new condition on the mapping f is provided