I will start the talk by introducing the different areas I am currently working in: the theory of partitions, mock theta functions, and analytic number theory. I will provide a brief yet accessible overview of these topics to ensure a broad audience can follow the discussion. Following this introduction, I will delve into one of my most exciting results on Koshliakov's zeta function arising from physics, outlining its motivation and significance. If time permits, I will also highlight some of my most recent findings. I will conclude the talk by presenting several open problems and potential future research directions, encouraging further exploration and collaboration in these areas.
This talk is based on three key research projects: my solo work, a collaborative project with Atul Dixit, and another joint work with Bruce C. Berndt and Atul Dixit.
