Values of certain Dirichlet series and higher derivative formulas of trigonometric functions

IF 0.5 3区数学 Q3 MATHEMATICS

International Journal of Number Theory Pub Date : 2024-03-13 DOI:10.1142/s1793042124500519

Dominic Lanphier, Allen Lin

引用次数: 0

Abstract

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.

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某些 Dirichlet 级数的值和三角函数的高导数公式

我们确定了某些 Dirichlet 级数和相关无穷级数的新值。这些公式扩展了多位学者的研究成果。为了得到这些结果，我们应用了三角函数高导数公式的最新展开式。我们还研究了这些级数值的超越性以及某些相关无穷级数值的算术关系。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

International Journal of Number Theory 数学-数学

CiteScore

1.10

自引率

14.30%

发文量

审稿时长

4-8 weeks

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.