7 papers
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…
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…
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…
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 this…
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…
Central Limit Theorem for the number of real roots of Kostlan Shub Smale random polynomial systems
Diego Armentano, Jean-Marc Azaïs, Federico Dalmao +1
We obtain a Central Limit Theorem for the normalized number of real roots of a square Kostlan-Shub-Smale random polynomial system of any size as the degree goes to infinity. A stud…