4 papers
Quasimodular forms that detect primes are Eisenstein
Jan-Willem van Ittersum, Lukas Mauth, Ken Ono +1
MacMahon's partition functions and their extensions provide equations that identify prime numbers as solutions. These results depend on the theory of (mixed weight) quasimodular fo…
Pentagonal number recurrence relations for
Kevin Gomez, Ken Ono, Hasan Saad +1
We revisit Euler's partition function recurrence, which asserts, for integers that $$ p(n)=p(n-1)+p(n-2)-p(n-5)-p(n-7)+\dots = \sum_{k\in \mathbb{Z}\setminus \{0\}} (-1)…
Distribution of hooks in self-conjugate partitions
William Craig, Ken Ono, Ajit Singh
We confirm the speculation that the distribution of -hooks among unrestricted integer partitions essentially descends to self-conjugate partitions. Namely, we prove that the num…
Traces of partition Eisenstein series
Tewodros Amdeberhan, Michael Griffin, Ken Ono +1
We study "partition Eisenstein series", extensions of the Eisenstein series defined by $$λ=(1^{m_1}, 2^{m_2},\dots, k^{m_k}) \vdash k \ \ \ \ \ \longmapsto \ \ \ \ \…