An Explicit Formula for the Local zeta Function of a Laurent Polynomial

Abstract

In a recent paper Zúñiga-Galindo and the author begun the study of the local zeta functions for Laurent polynomials. In this work we continue this study by giving a very explicit formula for the local zeta function associated to a Laurent polynomial $f$ over a $p-$adic field, when $f$ is weakly non-degenerate with respect to the Newton polytope of $f$ at infinity.

11 pages, 2 figures

References in corpus (3)

• Poles of Archimedean zeta functions for analytic mappings
• Local Zeta Functions for Non-degenerate Laurent Polynomials Over p-adic Fields
• Zeta functions and oscillatory integrals for meromorphic functions

Cited by in corpus (1)

• Bernstein-Sato polynomial and related invariants for meromorphic functions