梅尔卡关于涉及罗杰斯-拉马努扬函数的截断数列的一些猜想的证明

IF 0.9 2区数学 Q2 MATHEMATICS

Journal of Combinatorial Theory Series A Pub Date : 2024-09-19 DOI:10.1016/j.jcta.2024.105956

Yongqiang Chen, Olivia X.M. Yao

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引用次数: 0

摘要

2012 年，安德鲁斯和梅尔卡研究了欧拉五边形数定理的截断版本。他们的研究开启了截断θ级数的新研究，并激发了多位数学家对这一课题的研究。2019 年，Merca 研究了 Rogers-Ramanujan 函数，并就涉及 Rogers-Ramanujan 函数的截断数列提出了三组猜想。在本文中，我们根据 Pólya 和 Szegö 的一个结果，提出了证明 Merca 提出的三组猜想的统一方法。

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Proofs of some conjectures of Merca on truncated series involving the Rogers-Ramanujan functions

In 2012, Andrews and Merca investigated the truncated version of the Euler pentagonal number theorem. Their work has opened up a new study on truncated theta series and has inspired several mathematicians to work on the topic. In 2019, Merca studied the Rogers-Ramanujan functions and posed three groups of conjectures on truncated series involving the Rogers-Ramanujan functions. In this paper, we present a uniform method to prove the three groups of conjectures given by Merca based on a result due to Pólya and Szegö.

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来源期刊

Journal of Combinatorial Theory Series A 数学-数学

CiteScore

2.90

自引率

9.10%

发文量

审稿时长

12 months

期刊介绍： The Journal of Combinatorial Theory publishes original mathematical research concerned with theoretical and physical aspects of the study of finite and discrete structures in all branches of science. Series A is concerned primarily with structures, designs, and applications of combinatorics and is a valuable tool for mathematicians and computer scientists.