Partition congruences and the Andrews-Garvan-Dyson crank

被引:41
|
作者
Mahlburg, K [1 ]
机构
[1] Univ Wisconsin, Dept Math, Madison, WI 53706 USA
关键词
D O I
10.1073/pnas.0506702102
中图分类号
O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];
学科分类号
07 ; 0710 ; 09 ;
摘要
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.
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页码:15373 / 15376
页数:4
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