How Ramanujan May Have Discovered the Mock Theta Functions

Abstract: The mock theta functions made their first appearance in Ramanujan's last letter to Hardy. Ramanujan explains that he is trying to find functions apart from theta functions that behave like theta functions near the unit circle. Where did he ever get the idea that such functions might exist? Why in the world would he consider the special q-series that he lists in his last letter? The object of this talk is to provide a plausible explanation for the discovery of mock theta functions.

number theory

Audience: researchers in the topic

EIMI Number Theory Seminar

Series comments: Password: the number of quadratic nonresidues modulo 23