Modul:   MAT591  Discrete mathematics

The circle method with two variables

Vortrag von Dr. Jehanne Dousse

Datum: 01.03.16  Zeit: 11.15 - 12.15  Raum: Y27H28

The circle method was invented by Hardy and Ramanujan to compute the asymptotics for p(n), the number of partitions of n. More generally, it allows one to compute an asymptotic estimate of functions whose generating functions are modular forms. In this talk, I will present a two-variable generalisation of this method which allows one to compute the bivariate asymptotics of quantities whose generating functions are Jacobi or mock Jacobi forms. In particular I will show how it can be used to give an asymptotic formula for the crank and the rank of partitions, solving a 1989 conjecture of Freeman Dyson.