文献类型：期刊文献

英文题名：Evaluation of reciprocal sums of hyperbolic functions using quasimodular forms

作者：Wang, Wei[1]

机构：[1]Shaoxing Univ, Dept Math, Shaoxing 312000, Peoples R China

年份：2025

卷号：549

期号：2

外文期刊名：JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

收录：SCI-EXPANDED(收录号：WOS:001463064000001)、、Scopus(收录号：2-s2.0-105001570496)、WOS

基金：The author is supported by NSFC 11701272 and NSFC 12071221.

语种：英文

外文关键词：Hyperbolic functions; Complex multiplication; Quasimodular forms; Fibonacci zeta function

外文摘要：This paper studies eight families of infinite series involving hyperbolic functions. Under some conditions, these series are linear combinations of derivatives of Eisenstein series. Using complex multiplication theory, the structure of the rings of modular forms and quasimodular forms, and certain differential operators defined on these rings, this paper gives a systematic method for computing the values of these series at CM points. This paper also expresses the generalized reciprocal sums of Fibonacci numbers as the special values of the series mentioned above. Thus it gives some algebraic independence results about the generalized reciprocal sums of Fibonacci numbers. (c) 2025 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.