{"title":"某些 Dirichlet 级数的值和三角函数的高导数公式","authors":"Dominic Lanphier, Allen Lin","doi":"10.1142/s1793042124500519","DOIUrl":null,"url":null,"abstract":"<p>We determine new values of certain Dirichlet series and related infinite series. These formulas extend results of several authors. To obtain these results we apply recent expansions of higher derivative formulas of trigonometric functions. We also investigate the transcendentality of values of these series and arithmetic relations of the values of certain related infinite series.</p>","PeriodicalId":14293,"journal":{"name":"International Journal of Number Theory","volume":"22 1","pages":""},"PeriodicalIF":0.5000,"publicationDate":"2024-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Values of certain Dirichlet series and higher derivative formulas of trigonometric functions\",\"authors\":\"Dominic Lanphier, Allen Lin\",\"doi\":\"10.1142/s1793042124500519\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>We determine new values of certain Dirichlet series and related infinite series. These formulas extend results of several authors. To obtain these results we apply recent expansions of higher derivative formulas of trigonometric functions. We also investigate the transcendentality of values of these series and arithmetic relations of the values of certain related infinite series.</p>\",\"PeriodicalId\":14293,\"journal\":{\"name\":\"International Journal of Number Theory\",\"volume\":\"22 1\",\"pages\":\"\"},\"PeriodicalIF\":0.5000,\"publicationDate\":\"2024-03-13\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"International Journal of Number Theory\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1142/s1793042124500519\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Journal of Number Theory","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1142/s1793042124500519","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
Values of certain Dirichlet series and higher derivative formulas of trigonometric functions
We determine new values of certain Dirichlet series and related infinite series. These formulas extend results of several authors. To obtain these results we apply recent expansions of higher derivative formulas of trigonometric functions. We also investigate the transcendentality of values of these series and arithmetic relations of the values of certain related infinite series.
期刊介绍：
This journal publishes original research papers and review articles on all areas of Number Theory, including elementary number theory, analytic number theory, algebraic number theory, arithmetic algebraic geometry, geometry of numbers, diophantine equations, diophantine approximation, transcendental number theory, probabilistic number theory, modular forms, multiplicative number theory, additive number theory, partitions, and computational number theory.
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