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] Department of Mathematics, Shaoxing University, Shaoxing, 312000, China

年份：2023

外文期刊名：arXiv

收录：EI(收录号：20240013876)

语种：英文

外文关键词：Linear algebra - Mathematical operators

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.MSC Codes 11F25, 11J85 ? 2023, CC BY.