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arXiv · 2610.22111

The monodromy conjecture for high order poles, and norms of residue antiderivatives

Alexander Esterov
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Abstract

We prove the strong local monodromy conjecture for poles of order at least $n-1$ of the naive motivic zeta-function for a complex polynomial of $n$ variables. Moreover, for every such pole $s$, we construct an explicit homology $\exp(2πi s)$-eigencycle in a neighborhood of any given 1-dimensional exceptional stratum contributing the pole. The proof combines topological techniques developed by the author with a fact of birational geometry discovered by AI.

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Alexander Esterov. 2026-10-15. The monodromy conjecture for high order poles, and norms of residue antiderivatives. https://arxiv.org/abs/2610.22111

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