Alladi Ramakrishnan Hall

Inversion formulas for the j-function around elliptic points

Badri Vishal Pandey

University of Virginia

Recently, Hong, Mertens, Ono, and Zhang proved a conjecture of Caldararu, He, and Huang that expresses the Taylor series of the modular j-function around the elliptic points i and rho= e^{i pi/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.