Congruences for Frobenius Partitions

✍ Scribed by Ken Ono

• Book ID: 102600686
• Publisher: Elsevier Science
• Year: 1996
• Tongue: English
• Weight: 421 KB
• Volume: 57
• Category: Article
• ISSN: 0022-314X
• DOI: 10.1006/jnth.1996.0041

✦ Synopsis

The partition function p(n) has several celebrated congruence properties which reflect the action of the Hecke operators on certain holomorphic modular forms. In this article similar congruences are proved for c 3 (n), the number of generalized Frobenius partitions of n with 3 colors. We prove c 3 (63n+50)#0 mod 7,

(1)

exept when n=3T m and T m =m(m+1)Â2 is the m th triangular number, and

Congruences ( 2) and (3) are analogous to Euler's pentagonal number theorem. These congruences are proved by constructing holomorphic modular forms which inherit related congruence properties which are verified computationally via Sturm's criterion.