Computer Algebra Algorithms for Proving Jacobi Theta Function Relations
Dr. Liangjie Ye, RISC, Johannes Kepler University, Austria
【Abstract】This talk will be focused on proving Jacobi theta function identities. In the past centuries, many number theorists, e.g., Ramanujan, Hardy, Rademacher, Berndt, Borwein, etc., have proved a substantial amount of theta function relations by hand. There was no general method for proving such relations, and the computation in their proofs are usually tedious. Thanks to symbolic computation, now we have developed some computer algebra algorithms to prove and produce rich classes of such identities automatically. In this talk, I will present a nutshell of our research on this topic. I will also demonstrate a Mathematica package called ``ThetaFunctions" equipped with our algorithms.