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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2402.08007 |
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| _version_ | 1866929241930596352 |
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| author | Espinosa, Malors |
| author_facet | Espinosa, Malors |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_08007 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Zeta Functions of Certain Quadratic Orders Espinosa, Malors Number Theory 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. |
| title | Zeta Functions of Certain Quadratic Orders |
| topic | Number Theory |
| url | https://arxiv.org/abs/2402.08007 |