Speaker：Changgui Zhang (Lille University)

Time：2025-5-9, 14:30

Location：Conference Room C503 at Administration Building at Haiyun Campus 

Abstract:

In his final letter to Hardy in 1920, Ramanujan introduced functions he termed mock theta—families of analytic functions defined in the unit disk |q| < 1, but possessing infinitely many singularities on its boundary. they are expected to possess certain characteristic properties of a theta function in terms of their behavior near roots of unity.

In this talk, after reviewing connections between partitions, rank generating functions, and Appell-Lerch series, we will examine Ramanujan’s series as special values of solutions to linear q-difference equations that have a non-Fuchsian singularity at zero or infinity in the complex plane. The analysis of these singularities helps us understand the analytic structure of the governing equation and will lead us to different possible representations of a Ramanujan mock theta function. In particular, we will obtain certain modular-type relations in terms of the Stokes phenomenon, known for divergent series.