Atul Dixit (IIT, Gandhinagar) - Thursday, Mar 6, 2025 - 4:00 PM

 Dear all,

Next week's talk is by Atul Dixit of IIT, Gandhinagar. Here is the announcement. 

Talk Announcement: 

Title: The Rogers-Ramanujan dissection of a theta function

Speaker: Atul Dixit (IIT, Gandhinagar)
When: Mar 6, 2025, 4:00 PM- 5:00 PM IST (Our usual time)

Where: Zoom: Write to the organisers for the link

Live LInk: https://youtube.com/live/1v54wzJk-_o?feature=share

Abstract

Page 27 of Ramanujan's Lost Notebook contains a beautiful identity which, as shown by Andrews, not only gives a famous modular relation between the Rogers-Ramanujan functions $G(q)$ and $H(q)$ as a corollary but also a relation between two fifth order mock theta functions and $G(q)$ and $H(q)$. In this talk, we will discuss a generalization of Ramanujan's relation that we recently obtained which gives an infinite family of such identities. Our result shows that a theta function can always be ``dissected'' as a finite sum of products of generalized Rogers-Ramanujan functions. 

Several well-known results are shown to be consequences of our theorem, for example, a generalization of the Jacobi triple product identity and Andrews' relation between two of his generalized third order mock theta functions. As will be shown, the identities resulting from our main theorem for $s>2$ transcend the modular world and hence look difficult to be written in the form of a modular relation. Using asymptotic analysis, we also offer compelling evidence that explains how Ramanujan may have arrived at his generalized modular relation. This is joint work with Gaurav Kumar.