Frank Garvan

Extending Ramanujan’s Dyson rank function identity to all primes greater than 3


December 1, 2015, 3:00 — 3:50 pm at LIT 368.


Let \(R(z,q)\) be the two-variable generating function for Dyson’s rank function. In his lost notebook Ramanujan gives the 5-dissection of \(R(\zeta_p,q)\)
where \(\zeta_p\)  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.
We show that there is an analogous result for the \(p\)-dissection of \(R(\zeta_p,q)\) when \(p\) is any prime greater than 3.
This extends previous work of Bringmann and Ono, and Ahlgren and Treneer.