3 papers
math.NT2026
Euler-type Recurrence Relations for Partition Functions with Congruence Conditions
Wissam Raji, Hasan Saad
We study partition functions counting partitions into parts congruent to or . Using generalized Dedekind eta functions and Rankin-Cohen brackets, we…
math.NT2025
Atkin and Swinnerton-Dyer congruences for meromorphic modular forms
Michael Allen, Ling Long, Hasan Saad
In the 1970's, Atkin and Swinnerton-Dyer conjectured that Fourier coefficients of holomorphic modular cusp forms on noncongruence subgroups of satisfy cer…
math.NT2024
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)…