TY - JOUR
T1 - Congruence properties for the partition function
AU - Ahlgren, Scott
AU - Ono, Ken
PY - 2001/11/6
Y1 - 2001/11/6
N2 - 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.
AB - 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.
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U2 - 10.1073/pnas.191488598
DO - 10.1073/pnas.191488598
M3 - Article
C2 - 11606715
AN - SCOPUS:0035818476
SN - 0027-8424
VL - 98
SP - 12882
EP - 12884
JO - Proceedings of the National Academy of Sciences of the United States of America
JF - Proceedings of the National Academy of Sciences of the United States of America
IS - 23
ER -