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arXiv · 2509.03352

Birational zeta functions

Tom Biesbrouck·Nero Budur·Johannes Nicaise·Willem Veys
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Abstract

We define a birational analog of the motivic zeta function of a reduced polynomial in terms of minimal models. It admits an intrinsic meaning in terms of contact loci of arcs, an analog of a result of Denef and Loeser in the motivic case. We show that for local plane curve singularities the poles of the birational zeta function essentially coincide with the poles of the motivic zeta function.

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Tom Biesbrouck, Nero Budur, Johannes Nicaise, Willem Veys. 2025-09-03. Birational zeta functions. https://arxiv.org/abs/2509.03352

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