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Impacted Buildings for GL(2)

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 $SL(2, K)$.

preprint2026arXivOpen access
Malors EspinosaZander Karaganis
math.COmath.NT
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Malors EspinosaZander Karaganis

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