3流形的l -函数不变量及广义伯努利多项式之间的关系

IF 1.3 3区物理与天体物理 Q3 PHYSICS, MATHEMATICAL

Letters in Mathematical Physics Pub Date : 2025-02-28 DOI:10.1007/s11005-025-01912-5

Yuya Murakami

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引用次数: 0

摘要

我们引入了附在负定流形上的l函数作为同调块的Mellin变换。利用作者在前几篇论文中提出的渐近技术，证明了它们是整函数，并且它们在\( s=0 \)处的值等于Witten-Reshetikhin-Turaev不变量。我们还证明了一些l函数在负整数处的特殊值之间的线性关系，它们是Hurwitz zeta函数、Barnes zeta函数和Epstein zeta函数的一般推广。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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

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

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 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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来源期刊

Letters in Mathematical Physics 物理-物理：数学物理

CiteScore

2.40

自引率

8.30%

发文量

111

审稿时长

3 months

期刊介绍： The aim of Letters in Mathematical Physics is to attract the community''s attention on important and original developments in the area of mathematical physics and contemporary theoretical physics. The journal publishes letters and longer research articles, occasionally also articles containing topical reviews. We are committed to both fast publication and careful refereeing. In addition, the journal offers important contributions to modern mathematics in fields which have a potential physical application, and important developments in theoretical physics which have potential mathematical impact.