Abstract
The topological zeta function and Igusa's local zeta function are respectively a geometrical invariant associated to a complex polynomial f and an arithmetical invariant associated to a polynomial f over a p-adic field. When f is a polynomial in two variables we prove a formula for both zeta functions in terms of the so-called log canonical model of f-1{0} in A2. This result yields moreover a conceptual explanation for a known cancellation property of candidate poles for these zeta functions. Also in the formula for Igusa's local zeta function appears a remarkable non-symmetric ‘q-deformation’ of the intersection matrix of the minimal resolution of a Hirzebruch-Jung singularity. 1991 Mathematics Subject Classification: 32S50 11S80 14E30 (14G20)
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