Showing math.NTShow all
4 papers · 1 filter
math.NT2025
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…
math.NT2025
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…
math.NT2025
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…
math.NT2025
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…