Abstract:
:In 1944, Freeman Dyson conjectured the existence of a "crank" function for partitions that would provide a combinatorial proof of Ramanujan's congruence modulo 11. Forty years later, Andrews and Garvan successfully found such a function and proved the celebrated result that the crank simultaneously "explains" the three Ramanujan congruences modulo 5, 7, and 11. This note announces the proof of a conjecture of Ono, which essentially asserts that the elusive crank satisfies exactly the same types of general congruences as the partition function.
journal_name
Proc Natl Acad Sci U S Aauthors
Mahlburg Kdoi
10.1073/pnas.0506702102keywords:
subject
Has Abstractpub_date
2005-10-25 00:00:00pages
15373-6issue
43eissn
0027-8424issn
1091-6490pii
0506702102journal_volume
102pub_type
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