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Pure Mathematics 2026
两个涉及G？llnitz-Gordon函数的模关系
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Abstract:
G？llnitz-Gordon函数是整数分拆理论中非常重要的函数，它与著名的Rogers-Ramanujan恒等式密切相关。我们通过已知的连分数的2-剖分公式，通过奇偶分离的方法，得到了两个新的涉及G？llnitz-Gordon函数的模关系。
The G？llnitz-Gordon function is a crucial function in the theory of integer partitions, closely related to the renowned Rogers-Ramanujan identity. By utilizing the known 2-dissection formulas for continued fractions and employing the method of separating odd and even terms, we have derived two new modular relations involving theG？llnitz–Gordon functions.
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| [6] | Xia, E.X.W. and Yao, O.X.M. (2012) Some Modular Relations for the Göllnitz-Gordon Functions by An Even-Odd Method. Journal of Mathematical Analysis and Applications, 387, 126-138. https://doi.org/10.1016/j.jmaa.2011.08.059 |
