Congruences for Frobenius Partitions
Congruences for Frobenius Partitions
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DOI：
10.1006/jnth.1996.0041
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发表时间：
1996-03
影响因子：
0.7
通讯作者：
K. Ono
中科院分区：
文献类型：
--
作者：
K. Ono
Abstract The partition functionp(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 forc3(n), the number of generalized Frobenius partitions ofnwith 3 colors. We prove[formula]exept whenn=3TmandTm=m(m+1)/2 is themth triangular number, and[formula]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.
