5 papers
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…
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…
On Matrices Arising in Finite Field Hypergeometric Functions
Satoshi Kumabe, Hasan Saad
Lehmer constructs four classes of matrices constructed from roots of unity for which the characteristic polynomials and the -th powers can be determined explicitly. Here we stud…