New Modular Equations of Composite Degrees and Partition Identities

IF 1 3区数学 Q1 MATHEMATICS

Bulletin of the Malaysian Mathematical Sciences Society Pub Date : 2024-08-12 DOI:10.1007/s40840-024-01742-z

Roberta R. Zhou

引用次数: 0

Abstract

In a recent study, Kim established a general identity which implies a generalization of the modular equations of degrees 3, 5, 11 and 23, and derived some identities for partitions. In this paper we provide proofs for some new modular equations of composite degrees and degree of 7 by methods of elementary algebra and Kim’s generalization of theta-function identities. In addition, we derive many partition identities, which are proved depending upon these modular equations and reciprocation.

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复合度数的新模块方程和分部特征

在最近的一项研究中，Kim 建立了一个一般等式，它意味着 3、5、11 和 23 度模态方程的一般化，并导出了一些分部等式。在本文中，我们通过初等代数的方法和 Kim 对 Theta 函数等式的广义化，证明了一些新的复合度和 7 度的模方程。此外，我们还推导了许多分区等式，这些等式的证明依赖于这些模方程和倒数。

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

Bulletin of the Malaysian Mathematical Sciences Society 数学-数学

CiteScore

2.40

自引率

8.30%

发文量

176

审稿时长

3 months

期刊介绍： This journal publishes original research articles and expository survey articles in all branches of mathematics. Recent issues have included articles on such topics as Spectral synthesis for the operator space projective tensor product of C*-algebras; Topological structures on LA-semigroups; Implicit iteration methods for variational inequalities in Banach spaces; and The Quarter-Sweep Geometric Mean method for solving second kind linear fredholm integral equations.