Hypergeometric Motives from Euler Integral Representations
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866909971340328960 |
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| author | Kelly, Tyler L. Voight, John |
| author_facet | Kelly, Tyler L. Voight, John |
| contents | We revisit certain one-parameter families of affine covers arising naturally from Euler's integral representation of hypergeometric functions. We introduce a partial compactification of this family. We show that the zeta function of the fibers in the family can be written as an explicit product of $L$-series attached to nondegenerate hypergeometric motives and zeta functions of tori, twisted by Hecke Grossencharacters. This permits a combinatorial algorithm for computing the Hodge numbers of the family. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_03257 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Hypergeometric Motives from Euler Integral Representations Kelly, Tyler L. Voight, John Number Theory 11G40, 11S40, 11T24, 14C15, 14G10, 33C20 We revisit certain one-parameter families of affine covers arising naturally from Euler's integral representation of hypergeometric functions. We introduce a partial compactification of this family. We show that the zeta function of the fibers in the family can be written as an explicit product of $L$-series attached to nondegenerate hypergeometric motives and zeta functions of tori, twisted by Hecke Grossencharacters. This permits a combinatorial algorithm for computing the Hodge numbers of the family. |
| title | Hypergeometric Motives from Euler Integral Representations |
| topic | Number Theory 11G40, 11S40, 11T24, 14C15, 14G10, 33C20 |
| url | https://arxiv.org/abs/2412.03257 |