$L$-function invariants for 3-manifolds and relations between generalized Bernoulli polynomials

Yuya Murakami

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arXiv · 2410.05611

$L$-function invariants for 3-manifolds and relations between generalized Bernoulli polynomials

Yuya Murakami

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Abstract

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.

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BibTeX RIS

Yuya Murakami. 2024-10-08. $L$-function invariants for 3-manifolds and relations between generalized Bernoulli polynomials. https://arxiv.org/abs/2410.05611

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