From the 1 of 4 linked papers with an AI index.
4 papers
Euler-type Recurrence Relations for Partition Functions with Congruence Conditions
Wissam Raji, Hasan Saad
The paper investigates partition functions that count partitions with parts congruent to 0 or ±g modulo δ, deriving Euler‑type recurrence relations via generalized Dedekind eta fun…
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…
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 the Hessian values of Gaussian hypergeometric functions
Ken Ono, Sudhir Pujahari, Hasan Saad +1
We consider a special family of Gaussian hypergeometric functions whose entries are cubic and trivial characters over finite fields. The special values of these functions are known…