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arXiv · 2402.08007

Zeta Functions of Certain Quadratic Orders

Malors Espinosa
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Abstract

Langlands provides a formula for certain product of orbital integrals in $GL(2, \mathbb{Q})$. Its generalization has become an important question for the strategy of Beyond Endoscopy. Arthur predicts this formula should coincide with a product of polynomials associated to zeta functions of orders constructed by Zhiwei Yun. In this paper we compute, for a certain family of orders, explicit formulas for these zeta functions by a recursive method. We use these zeta functions in a further paper to prove that Arthur's prediction is correct.

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Malors Espinosa. 2024-02-12. Zeta Functions of Certain Quadratic Orders. https://doi.org/10.1016/j.jnt.2023.06.002

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