Impacted Buildings for GL(2)
Abstract
In this paper we define a generating function for buildings of type $\widetilde{A}_1$ (i.e. trees) that are enhanced with a certain filtration structure. We prove that this generating function recovers the zeta function of certain quadratic orders. We do this by studying how the ideals of the orders distribute in the building of $SL(2, K)$.
Fields of Study & Subjects
Advanced Algebra and Geometry
Analytic Number Theory Research
Algebraic Geometry and Number Theory
Publication details
- Journal / source
- arXiv (Cornell University)
- Publication date
- 13 January 2026
- Document type
- Preprint