光谱行列式的递推公式

IF 0.6 3区数学 Q3 MATHEMATICS

Journal of Number Theory Pub Date : 2024-09-20 DOI:10.1016/j.jnt.2024.08.004

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引用次数: 0

摘要

我们开发了一种统一的方法来研究几种不同流形（包括球面和半球面以及投影空间）的谱行列式。这是基于推导相应zeta函数递推关系的方法的直接结果，然后我们就能明确地求解这些递推关系。除了半球等新应用之外，我们还认为，在行列式表达式已经已知的情况下，与其他方法得出的公式相比，我们得出的公式更简单，更易于计算。

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Recurrence formulae for spectral determinants

We develop a unified method to study spectral determinants for several different manifolds, including spheres and hemispheres, and projective spaces. This is a direct consequence of an approach based on deriving recursion relations for the corresponding zeta functions, which we are then able to solve explicitly. Apart from new applications such as hemispheres, we also believe that the resulting formulae in the cases for which expressions for the determinant were already known are simpler and easier to compute in general, when compared to those resulting from other approaches.

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来源期刊

Journal of Number Theory 数学-数学

CiteScore

1.30

自引率

14.30%

发文量

122

审稿时长

16 weeks

期刊介绍： The Journal of Number Theory (JNT) features selected research articles that represent the broad spectrum of interest in contemporary number theory and allied areas. A valuable resource for mathematicians, the journal provides an international forum for the publication of original research in this field. The Journal of Number Theory is encouraging submissions of quality, long articles where most or all of the technical details are included. The journal now considers and welcomes also papers in Computational Number Theory. Starting in May 2019, JNT will have a new format with 3 sections: JNT Prime targets (possibly very long with complete proofs) high impact papers. Articles published in this section will be granted 1 year promotional open access. JNT General Section is for shorter papers. We particularly encourage submission from junior researchers. Every attempt will be made to expedite the review process for such submissions. Computational JNT . This section aims to provide a forum to disseminate contributions which make significant use of computer calculations to derive novel number theoretic results. There will be an online repository where supplementary codes and data can be stored.