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arXiv · 1702.06938

Local Zeta Functions for Rational Functions and Newton Polyhedra

Miriam Bocardo-Gaspar·W. A. Zúñiga-Galindo
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Abstract

In this article, we introduce a notion of non-degeneracy, with respect to certain Newton polyhedra, for rational functions over non-Archimedean locals fields of arbitrary characteristic. We study the local zeta functions attached to non-degenerate rational functions, we show the existence of a meromorphic continuation for these zeta functions, as rational functions of $q^{-s}$, and give explicit formulas. In contrast with the classical local zeta functions, the meromorphic continuation of zeta functions for rational functions have poles with positive and negative real parts.

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Miriam Bocardo-Gaspar, W. A. Zúñiga-Galindo. 2017-02-22. Local Zeta Functions for Rational Functions and Newton Polyhedra. https://arxiv.org/abs/1702.06938

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