# Meeting Details

Title: Cubic Theta Functions in Two Variables Combinatorics/Partitions Seminar Daniel Schultz, PSU By adding certain equianharmonic elliptic sigma functions to the coefficients of the Borwein cubic theta functions, an interesting set of six two-variable theta functions may be derived. These theta functions invert the $F_1\left( \frac{1}{3};\frac{1}{3};\frac{1}{3};1 |x,y \right)$ case of Appell's hypergeometric function and satisfy several identities akin to those satisfied by the Borwein cubic theta functions. The work of Koike et al. is extended and put into the context of modular equations, resulting in a simpler derivation of their results as well as several new modular equations for Picard modular forms.