| 摘要: |
| 本文研究了若干特殊的theta函数和q-级数.利用它们定义的特殊形式，建立了几类特殊的q-级数与Ramanujan Tau函数的生成函数的关系，从而得到了几个Ramanujan Tau函数新的显式表达式.最后作为定理的应用，还得到了一个有关Ramanujan Tau函数的同余恒等式. |
| 关键词: theta函数 q-级数 Ramanujan Tau函数 |
| DOI： |
| 分类号:O156 |
| 基金项目:四川省教育厅科研基金资助（15ZB0434）. |
|
| A NOTE ON THE RAMANUJAN'S TAU FUNCTION |
|
CHENG Kai-min
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College of Mathematics and Information, China West Normal University, Nanchong 637002, China
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| Abstract: |
| In this paper, we study several theta functions and q-series. Utilizing the special forms of their definitions, we construct some relations between some q-series and the Ramanujan's tau function. In particular, we obtain two new explicit expressions for the Ramanujan's tau function. Lastly, as the application of our theorem, we get a new congruence of Ramanujan's tau function. |
| Key words: theta functions q-series the Ramanujan's Tau function |
