论文标题
$ j $功能围绕椭圆点的倒置公式
Inversion Formulas for the $j$-function Around Elliptic Points
论文作者
论文摘要
最近，Hong，Mertens，Ono和Zhang证明了Căldăraru，He和Huang的猜想，在椭圆点$ i $和$ j $ i $和$ρ= e^{πi/3} $的taylor系列中表达了taylor系列，因为与nightation cansation cansation cansature 2案例和3案例均为Ramanuip eell asterations farsiations y raman eell asteration and eell and eell eell eell and eell eell and eell eell eell eell。我们扩展了这些结果，并为$ j $ function提供$ i $和$ρ$的反转公式，由高斯的超几何功能以及签名4和6中的Ramanujan的理论产生。
Recently, Hong, Mertens, Ono and Zhang proved a conjecture of Căldăraru, He, and Huang that expresses the Taylor series of the modular $j$-function around the elliptic points $i$ and $ρ=e^{πi/3}$ as rational functions arising from the signature 2 and 3 cases of Ramanujan's theory of elliptic functions to alternative bases. We extend these results and give inversion formulas for the $j$-function around $i$ and $ρ$ arising from Gauss' hypergeometric functions and Ramanujan's theory in signatures 4 and 6.
