On the Siegel series in terms of lattice counting
Abstract
In this paper, we describe each coefficient of the Siegel series associated to a quadratic o-lattice L in terms of lattice counting problems, where o is the ring of integers of a non-Archimedean local field of characteristic 0. Under the restriction that p is odd and that the dimension of the radical of the quadratic space L⊗κ on the residue field κ is at most 2, we provide explicit values of coefficients and reprove the functional equation of the Siegel series.
Fields of Study & Subjects
Advanced Mathematical Identities
Advanced Algebra and Geometry
Mathematical Dynamics and Fractals
Publication details
- Journal / source
- Kyoto journal of mathematics
- Publisher
- Duke University Press
- Volume
- -1
- Issue
- -1
- Pages
- 1–26
- Publication date
- 1 January 2026
- Language
- EN