$L$-function invariants for 3-manifolds and relations between generalized Bernoulli polynomials
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866917796536909824 |
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| author | Murakami, Yuya |
| author_facet | Murakami, Yuya |
| contents | We introduce $ L $-functions attached to negative definite plumbed manifolds as the Mellin transforms of homological blocks. We prove that they are entire functions and their values at $ s=0 $ are equal to the Witten--Reshetikhin--Turaev invariants by using asymptotic techniques developed by the author in the previous papers. We also prove that linear relations between special values at negative integers of some $ L $-functions, which are common generalizations of Hurwitz zeta functions, Barnes zeta functions and Epstein zeta functions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_05611 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | $L$-function invariants for 3-manifolds and relations between generalized Bernoulli polynomials Murakami, Yuya Geometric Topology Number Theory Quantum Algebra 57K31, 57K10, 57K16, 11F27, 11B68, 11E45 We introduce $ L $-functions attached to negative definite plumbed manifolds as the Mellin transforms of homological blocks. We prove that they are entire functions and their values at $ s=0 $ are equal to the Witten--Reshetikhin--Turaev invariants by using asymptotic techniques developed by the author in the previous papers. We also prove that linear relations between special values at negative integers of some $ L $-functions, which are common generalizations of Hurwitz zeta functions, Barnes zeta functions and Epstein zeta functions. |
| title | $L$-function invariants for 3-manifolds and relations between generalized Bernoulli polynomials |
| topic | Geometric Topology Number Theory Quantum Algebra 57K31, 57K10, 57K16, 11F27, 11B68, 11E45 |
| url | https://arxiv.org/abs/2410.05611 |