The Igusa Zeta function of restricted power series over ℚ_p

2025/04/24 by Leonie Dausy, Dausy, Leonie
Mathematics · #Advanced Mathematical Identities #Approximation Theory and Sequence Spaces #FOS: Mathematics #Number Theory (math.NT) #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2504.17687

openalex publication_date 2025/04/24 · openalex created_date 2025/10/18 · openalex updated_date 2026/07/28

Abstract

In this article, we ask whether the Igusa zeta function of a restricted power series over ℚ_p can be determined solely from the terms of degree at most D. That is, we ask whether the truncated polynomial f_D, consisting of all terms of f of degree ≤ D, yields the same Igusa zeta function as f for sufficiently large D. Our main results include a counterexample already in the one-variable case, but also a positive result under the condition that f is sufficiently non-degenerate with respect to its Newton polyhedron Γ(f).

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