On the smallest poles of Igusa's p-adic zeta functions
Number Theory
2007-05-23 v1 Algebraic Geometry
Abstract
Let K be a p-adic field. We explore Igusa's p-adic zeta function, which is associated to a K-analytic function on an open and compact subset of K^n. First we deduce a formula for an important coefficient in the Laurent series of this meromorphic function at a candidate pole. Afterwards we use this formula to determine all values less than -1/2 for n=2 and less than -1 for n=3 which occur as the real part of a pole.
Cite
@article{arxiv.math/0509042,
title = {On the smallest poles of Igusa's p-adic zeta functions},
author = {Dirk Segers},
journal= {arXiv preprint arXiv:math/0509042},
year = {2007}
}
Comments
27 pages