Inversion Formulas for the $j$-function Around Elliptic Points
| Autor: | Alejandro De Las Penas Castano, Badri Vishal Pandey |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2022 |
| Předmět: | |
| Popis: | Recently, Hong, Mertens, Ono and Zhang proved a conjecture of C\u{a}ld\u{a}raru, He, and Huang that expresses the Taylor series of the modular $j$-function around the elliptic points $i$ and $\rho=e^{\pi i/3}$ 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 $\rho$ arising from Gauss' hypergeometric functions and Ramanujan's theory in signatures 4 and 6. Comment: 9 pages |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|