The spt and unimodal sequence conjectures

Abstract: In 2012 Bryson, Ono, Pitman, and Rhoades showed how the generating functions for certain strongly unimodal sequences are related to quantum modular and mock modular forms. They proved some parity results and conjectured some mod 4 congruences for the coefficients of these generating functions. In 2016 Kim, Lim and Lovejoy obtained similar results for odd-balanced unimodal sequences and made similar mod 4 conjectures. In 2017 the speaker made some similar conjectures for the Andrews spt-function. In this talk, we outline how to prove these conjectures. This involves a connection between the Hurwitz class number function and Ramanujan's mock theta functions. This is joint work with Rong Chen (Shanghai).

number theory

Audience: researchers in the discipline

Dublin Algebra and Number Theory Seminar

Series comments: Passcode: The 3-digit prime numerator of Riemann zeta at -11