Partial theta series with periodic coefficients and quantum modular forms

Abstract: Theta series first appeared in Euler’s work on partitions, but was systematically studied later by Jacobi. In his Lost Notebook, Ramanujan wrote down many identities (without proof) involving the so-called partial theta series. Unlike the theta series which are modular forms, the theory of partial theta series is not well understood. In this talk, I will consider a family of partial theta series and show their “quantum modular” behaviour. This is based on my recent joint work with Robert Osburn (UCD).

The talk should be accessible to graduate and advanced undergraduate students.

classical analysis and ODEscombinatoricsnumber theory

Audience: researchers in the topic

Special Functions and Number Theory seminar

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