Series for $1/\pi$ of signature 20

Abstract

Properties of theta functions and Eisenstein series dating to Jacobi and Ramanujan are used to deduce differential equations associated with McKay Thompson series of level 20. These equations induce expansions for modular forms of level 20 in terms of modular functions.The theory of singular values is applied to derive expansions for $1/\pi$ of signature $20$ analogous to those formulated by Ramanujan.