Ahlgren S, Ono K
Department of Mathematics, University of Illinois, Urbana, IL 61801, USA.
Proc Natl Acad Sci U S A. 2001 Nov 6;98(23):12882-4. doi: 10.1073/pnas.191488598. Epub 2001 Oct 23.
Eighty years ago, Ramanujan conjectured and proved some striking congruences for the partition function modulo powers of 5, 7, and 11. Until recently, only a handful of further such congruences were known. Here we report that such congruences are much more widespread than was previously known, and we describe the theoretical framework that appears to explain every known Ramanujan-type congruence.
八十年前，拉马努金猜想并证明了一些关于分拆函数模5、7和11的幂的惊人同余式。直到最近，人们只知道少数几个这样的同余式。在此我们报告，这类同余式比之前所知的更为普遍，并且我们描述了一个似乎能解释每一个已知的拉马努金型同余式的理论框架。
