Dear All,
The talk in the coming week will be delivered by Rishabh Sarma, S. Chowla Research Assistant Professor of the Department of Mathematics at Pennsylvania State University.
Talk Announcement:
Title: Modular symmetries for rank and crank statistics
Title: Modular symmetries for rank and crank statistics
Speaker: Rishabh Sarma, Pennsylvania State University.
When: June 18, 2026, 6:00 PM- 7:00 PM IST
When: June 18, 2026, 6:00 PM- 7:00 PM IST
Where: Zoom: Write to the SFNT organizers.
Abstract
Let R(z,q) be the two-variable generating function for Dyson’s rank function. In his lost notebook Ramanujan gives the p-dissection of R(ζp,q) where ζp is a primitive p-th root of unity and p=5. This result is related to Dyson’s famous rank conjecture which was proved by Atkin and Swinnerton-Dyer. In this talk, we explore the modular structure of this function, the partition crank and their overpartition counterparts, leading to a symmetry phenomenon among the elements of the p-dissection of these functions.
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Gaurav Bhatnagar, Atul Dixit, Bibekananda Maji, Krishnan Rajkumar, and Manjil Saikia
Special Functions and Number Theory Seminar
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