The Igusa Zeta function of restricted power series over $\mathbb{Q}_p$
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866915257158467584 |
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| author | Dausy, Leonie |
| author_facet | Dausy, Leonie |
| contents | In this article, we ask whether the Igusa zeta function of a restricted power series over $\mathbb{Q}_p$ 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 $\leq D$, 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 $Γ(f)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_17687 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Igusa Zeta function of restricted power series over $\mathbb{Q}_p$ Dausy, Leonie Number Theory In this article, we ask whether the Igusa zeta function of a restricted power series over $\mathbb{Q}_p$ 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 $\leq D$, 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 $Γ(f)$. |
| title | The Igusa Zeta function of restricted power series over $\mathbb{Q}_p$ |
| topic | Number Theory |
| url | https://arxiv.org/abs/2504.17687 |