Goillnitz Gordon函数相关函数的新模关系及证明

Some New Modular Relations of Gollnitz-Gordon Function Correlation Function and Its Proof

摘要: 本文出于对数论中Gollnitz-Gordon函数模关系的研究学习，发现了关于该函数的相关函数S(-q)还存在许多类似的模关系。为了找出某些新的模关系，本文利用了Schroter的数学公式和Ramanujan提出的一些简单的θ函数恒等式来进行推导转化，通过该方法建立了两个与S(−q)相关的新模关系并给出了证明，这两个新模关系是对已知模关系的扩展，该发现有助于之后读者在数论学习中对模关系进行研究及学习。

Abstract: Based on the study of the modular relation of Gollnitz-Gordon function in number theory, we find that there are many similar modular relations about the correlation function S(−q) of Gollnitz-Gordon function. In order to find out some new modular relations, Schroter’s mathematical formula and some simple θ function identities proposed by Ramanujan were used for derivation and transformation. Through this method, two new modular relations related to S(-q) were established and proved. The two new modular relations are extensions of the known modular re-lations. This finding is helpful for readers to study and learn modular relations in the study of number theory.