Zeta Functions for Non-degenerate Laurent Polynomials Over p-adic Fields

Details Zeta Functions for Non-degenerate Laurent Polynomials Over p-adic Fields Zeta Functions for Non-degenerate Laurent Polynomials Over p-adic Fields

2010-09-20

arxiv.org/abs/1009.3680v2

Mathematics

Algebraic Geometry

Seveal typos and small erors were corrected

Scientific paper

We study local zeta functions for non-degenerate Laurent polynomials over p-adic fields. The main result is the existence of asymptotic expansions for exponential sums mod p^{m}, or more generally, for p-adic oscillatory integrals attached to Laurent polynomials. We show the existence of two different asymptotic expansions: 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.

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