On the smallest poles of Igusa's p-adic zeta functions

Details On the smallest poles of Igusa's p-adic zeta functions On the smallest poles of Igusa's p-adic zeta functions

2005-09-02

arxiv.org/abs/math/0509042v1

Math. Zeitschrift 252, 429-455 (2006)

Mathematics

Number Theory

27 pages

Scientific paper

10.1007/s00209-005-0864-z

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.

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