# Almost non-degenerate functions and a Zariski pair of links

### Mutsuo Oka

Tokyo University of Science, Japan

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## Abstract

Let $f(z)$ be an analytic function defined in the neighborhood of the origin of $C_{n}$ which have some Newton degenerate faces. We generalize the Varchenko formula for the zeta function of the Milnor fibration of a Newton non-degenerate function $f$ to this case. As an application, we give an example of a pair of hypersurfaces with the same Newton boundary and the same zeta function with different tangent cones.