[Abstract] Jie Frye and Frank Garvan; Automatic Proof of Theta-Function Identities, in "Elliptic Integrals, Elliptic Functions and Modular Forms in Quantum Field Theory", Texts Monogr. Symbol. Comput.,Springer, Cham,2019, pp.195-258.


Abstract:

This is a tutorial for using two new MAPLE packages, thetaids and ramarobinsids. The thetaids package is designed for proving generalized eta-product identities using the valence formula for modular functions. We show how this package can be used to find theta-function identities as well as prove them. As an application, we show how to find and prove Ramanujan's 40 identities for his so called Rogers-Ramanujan functions G(q) and H(q). In his thesis Robins found similar identities for higher level generalized eta-products. Our ramarobinsids package is for finding and proving identities for generalizations of Ramanujan's G(q) and H(q) and Robin's extensions. These generalizations are associated with certain real Dirichlet characters. We find a total of over 150 identities.

The url of this page is http://www.math.ufl.edu/~fgarvan/abstracts/auto-theta.html.
Created by F.G. Garvan (fgarvan@ufl.edu) on Friday, July 20, 2018.
Last update made Tue Aug 20 12:15:17 EDT 2019.

MAIL fgarvan@ufl.edu