{"title":"谱zeta函数的特殊值与组合学：Sturm-Liouville 问题","authors":"Bing Xie , Yigeng Zhao , Yongqiang Zhao","doi":"10.1016/j.ejc.2024.103972","DOIUrl":null,"url":null,"abstract":"<div><p>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.</p></div>","PeriodicalId":50490,"journal":{"name":"European Journal of Combinatorics","volume":null,"pages":null},"PeriodicalIF":1.0000,"publicationDate":"2024-04-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Special values of spectral zeta functions and combinatorics: Sturm–Liouville problems\",\"authors\":\"Bing Xie , Yigeng Zhao , Yongqiang Zhao\",\"doi\":\"10.1016/j.ejc.2024.103972\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>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.</p></div>\",\"PeriodicalId\":50490,\"journal\":{\"name\":\"European Journal of Combinatorics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.0000,\"publicationDate\":\"2024-04-16\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"European Journal of Combinatorics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S019566982400057X\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"European Journal of Combinatorics","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S019566982400057X","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
Special values of spectral zeta functions and combinatorics: Sturm–Liouville problems
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.
期刊介绍：
The European Journal of Combinatorics is a high standard, international, bimonthly journal of pure mathematics, specializing in theories arising from combinatorial problems. The journal is primarily open to papers dealing with mathematical structures within combinatorics and/or establishing direct links between combinatorics and other branches of mathematics and the theories of computing. The journal includes full-length research papers on important topics.
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