International Seminar on Automorphic Forms

Qihang Sun (University of Lille): Exact formulae for ranks of partitions

Dyson’s ranks provided a new understanding of the integer partition function, especially of its congruence properties. In 2009, Bringmann used the circle method to prove an asymptotic formula for the Fourier coefficients of rank generating functions. In this talk, we will prove that the asymptotic formula, when summing up to infinity, converges and becomes a Rademacher-type exact formula for the rank of partitions.

https://tu-darmstadt.zoom.us/j/68048280736