Poles of real motivic zeta functions for curves
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arXiv
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866908748353634304 |
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| author | Jaudon, Théo |
| author_facet | Jaudon, Théo |
| contents | To a given real polynomial function f $\in$ R[x1, . . . , x d ], we associate real topological zeta functions Ztop,0(f\,; s) and Z $\pm$ top,0 (f\,; s) $\in$ Q(s), analogous to the topological zeta function of Denef and Loeser in the complex case. These functions are specializations of the real motivic zeta functions studied in [Fic05a] and [Cam17]. Therefore, these functions and their sets of poles are invariants of the blow-Nash equivalence. Using the approach of [Vey95], we study the poles of these real topological zeta functions, as well as real motivic zeta functions, when f is a real polynomial in two variables. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_02180 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Poles of real motivic zeta functions for curves Jaudon, Théo Algebraic Geometry To a given real polynomial function f $\in$ R[x1, . . . , x d ], we associate real topological zeta functions Ztop,0(f\,; s) and Z $\pm$ top,0 (f\,; s) $\in$ Q(s), analogous to the topological zeta function of Denef and Loeser in the complex case. These functions are specializations of the real motivic zeta functions studied in [Fic05a] and [Cam17]. Therefore, these functions and their sets of poles are invariants of the blow-Nash equivalence. Using the approach of [Vey95], we study the poles of these real topological zeta functions, as well as real motivic zeta functions, when f is a real polynomial in two variables. |
| title | Poles of real motivic zeta functions for curves |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2601.02180 |