Speaker : Prof. Zhiguo Liu (East China Normal University) Title : Elliptic theta functions and Ramanujan series for $1/\pi$ Time : 2017-07-18 (Tue) 15:00 - Place : Seminar Room 722, Institute of Mathematics (NTU Campus) Abstract: In his 1914 paper "Modular Equations and Approximations to $\pi$", Ramanujan listed a total of $17$ series for $1/\pi.$ Ramanujan did not indicate how he arrived at these series but instead hinted that some of these series belonged to the theories of elliptic functions to alternative bases. In 1987, Jonathan and Peter Borwein provided rigorous proofs of Ramanujan for all 17 of Ramanujan’s series for $1/\pi$. The proofs of these series require a profound knowledge of number theory such as modular forms and class invariants. In this talk, I will illustrate with an example that one can derive Ramanujan series only using elliptic theta functions. I will give as many details as possible.