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arXiv · 2601.08365

Impacted Buildings for GL(2)

Malors Espinosa·Zander Karaganis
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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 $SL(2, K)$.

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Malors Espinosa, Zander Karaganis. 2026-01-13. Impacted Buildings for GL(2). https://arxiv.org/abs/2601.08365

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