Multiple Dirichlet series associated with quadrics
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866929206724657152 |
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| author | Wen, Jun |
| author_facet | Wen, Jun |
| contents | We define a multiple Dirichlet series associated with quadrics which is the zero locus of a quadratic form. This multiple Dirichlet series is linked to a Shintani zeta function associated with a prehomogeneous vector space. To obtain the functional equations we construct a filtration of the quadratic space and define the parabolic group actions, and then apply a non-abelian Poisson summation formula which sums over all lower dimensional quadrics along with the original quadrics. We show the group of functional equations is isomorphic to a finite Weyl group of type A3. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_05729 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Multiple Dirichlet series associated with quadrics Wen, Jun Number Theory We define a multiple Dirichlet series associated with quadrics which is the zero locus of a quadratic form. This multiple Dirichlet series is linked to a Shintani zeta function associated with a prehomogeneous vector space. To obtain the functional equations we construct a filtration of the quadratic space and define the parabolic group actions, and then apply a non-abelian Poisson summation formula which sums over all lower dimensional quadrics along with the original quadrics. We show the group of functional equations is isomorphic to a finite Weyl group of type A3. |
| title | Multiple Dirichlet series associated with quadrics |
| topic | Number Theory |
| url | https://arxiv.org/abs/2401.05729 |