Special values of spectral zeta functions and combinatorics: Sturm-Liouville problems
Combinatorics
2024-04-02 v2 Number Theory
Spectral Theory
Abstract
In this paper, we apply the combinatorial results on counting permutations with fixed pinnacle and vale sets to evaluate the special values of the spectral zeta functions of Sturm-Liouville differential operators. As applications, we get a combinatorial formula for the special values of spectral zeta functions and give a new explicit formula for Bernoulli numbers.
Keywords
Cite
@article{arxiv.2303.10004,
title = {Special values of spectral zeta functions and combinatorics: Sturm-Liouville problems},
author = {Bing Xie and Yigeng Zhao and Yongqiang Zhao},
journal= {arXiv preprint arXiv:2303.10004},
year = {2024}
}