2 papers
math.NT2025
Ramanujan's partition generating functions modulo
Kathrin Bringmann, William Craig, Ken Ono
For the partition function , Ramanujan proved the striking identities $$ P_5(q):=\sum_{n\geq 0} p(5n+4)q^n =5\prod_{n\geq 1} \frac{\left(q^5;q^5\right)_{\infty}^5}{(q;q)_{\in…
math.NT2024
Integer partitions detect the primes
William Craig, Jan-Willem van Ittersum, Ken Ono
We show that integer partitions, the fundamental building blocks in additive number theory, detect prime numbers in an unexpected way. Answering a question of Schneider, we show th…