论文标题
Ramanujan的单数模式和Ramanujan- Selberg的明确评估公式继续
The Explicit Evaluations Formula for Ramanujan's Singular Moduli and Ramanujan- Selberg Continued Fraction
论文作者
论文摘要
在他笔记本的分散位置，Ramanujan录制了30多个奇异模量$α_n$的值。所有这些结果均由Berndt ET证明。 Al使用Weber-Ramanujan的班级不变。在本文中，我们通过涉及班级不变性来得出$α__{9n} $和$α_{n/9} $的显式评估公式。为此，我们建立了涉及theta功能的几个新的$ p-q $混合模块化方程。这些模块化方程的进一步应用，我们得出了一个新的公式，以明确评估Ramanujan-Selberg继续分数。
At scattered places of his notebooks, Ramanujan recorded over 30 values of singular moduli $α_n$. All those results were proved by Berndt et. al by employing Weber-Ramanujan's class invariants. In this paper, we initiate to derive the explicit evaluations formula for $α_{9n}$ and $α_{n/9}$ by involving class invariant. For this purpose, we establish several new $P-Q$ mixed modular equations involving theta-functions. Further application of these modular equations, we derive a new formula to explicit evaluation of Ramanujan- Selberg continued fraction.
