Cyclic Identities Involving Ratios of Jacobi Theta Functions
  Identities involving cyclic sums of terms composed from Jacobi elliptic functions evaluated at $p$ equally shifted points were recently found. The purpose of this paper is to re-express these cyclic identities in terms of ratios of Jacobi theta functions, since many physicists prefer using Jacobi theta functions rather than Jacobi elliptic functions. 
Avinash Khare, Arul Lakshminarayan, Uday Sukhatme