6 papers
The partition function and elliptic curves
Ken Ono
The Bruinier-Ono formula expresses the partition number as a trace of `non-holomorphic' singular moduli of discriminant CM points on We interpret thi…
Modular forms for chromatic homotopy: Supersingular congruences
Ken Ono
We prove a conjecture of Larson in Behrens' program on congruences of modular forms attached to the divided beta family in the Adams--Novikov spectral sequence for the stable homot…
Modularity from -series
Ken Ono
In 1975, G. E. Andrews challenged the mathematics community to address L. Ehrenpreis' problem, which was to directly prove the modularity of the Rogers-Ramanujan -series' summat…
Hermite-Jensen limits and log-concavity of -multinomials
Ken Ono
In 1878, Sylvester proved Cayley's Conjecture that the coefficients of the Gaussian -binomial coefficients are unimodal. In 1990, O'Hara famously discovered a constructive combi…
Partition functions that repel perfect-powers
Ken Ono
A conjecture by Sun states that the partition function , for , is never a perfect power. Recent work by Merca et al. proposes generalizations of perfect-power repulsion…
Do perfect powers repel partition numbers?
Mircea Merca, Ken Ono, Wei-Lun Tsai
In 2013 Zhi-Wei Sun conjectured that is never a power of an integer when We confirm this claim in many cases. We also observe that integral powers appear to repel the…