赫克型双和与贝利变换

The Ramanujan Journal Pub Date : 2024-08-22 DOI:10.1007/s11139-024-00926-2

Su-Ping Cui, Hai-Xing Du, Nancy S. S. Gu, Liuquan Wang

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引用次数: 0

摘要

在证明拉马努扬给出的许多与模拟 Theta 函数相关的等式时，Hecke 型双和起着至关重要的作用。在文献中，贝利对机制是推导模拟 Theta 函数的 Hecke 型双和的有效工具。在本文中，我们利用一些贝利对和共轭贝利对，然后应用贝利变换，建立了一些三变量等式，这些等式隐含了一些阶数为 3、6 和 10 的经典模拟 Theta 函数的 Hecke 型双和。同时，我们还推广了加尔文提出的一个双变量 Hecke 型特性。

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Hecke-type double sums and the Bailey transform

Hecke-type double sums play a crucial role in proving many identities related to mock theta functions given by Ramanujan. In the literature, the Bailey pair machinery is an efficient tool to derive Hecke-type double sums for mock theta functions. In this paper, by using some Bailey pairs and conjugate Bailey pairs, and then applying the Bailey transform, we establish some trivariate identities which imply the Hecke-type double sums for some classical mock theta functions of orders 3, 6, and 10. Meanwhile, we generalize a bivariate Hecke-type identity due to Garvan.

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The Ramanujan Journal

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