Poles of real motivic zeta functions for curves
Algebraic Geometry
2026-01-06 v1
Abstract
To a given real polynomial function f R[x1, . . . , x d ], we associate real topological zeta functions Ztop,0(f\,; s) and Z top,0 (f\,; s) 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.
Cite
@article{arxiv.2601.02180,
title = {Poles of real motivic zeta functions for curves},
author = {Théo Jaudon},
journal= {arXiv preprint arXiv:2601.02180},
year = {2026}
}