Special values of spectral zeta functions and combinatorics: Sturm-Liouville problems
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866910391435526144 |
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| author | Xie, Bing Zhao, Yigeng Zhao, Yongqiang |
| author_facet | Xie, Bing Zhao, Yigeng Zhao, Yongqiang |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_10004 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Special values of spectral zeta functions and combinatorics: Sturm-Liouville problems Xie, Bing Zhao, Yigeng Zhao, Yongqiang Combinatorics Number Theory Spectral Theory Primary 05A05, Secondary 11M06, 34B24 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. |
| title | Special values of spectral zeta functions and combinatorics: Sturm-Liouville problems |
| topic | Combinatorics Number Theory Spectral Theory Primary 05A05, Secondary 11M06, 34B24 |
| url | https://arxiv.org/abs/2303.10004 |