The f(q) mock theta function conjecture and partition ranks

  title={The f(q) mock theta function conjecture and partition ranks},
  author={Kathrin Bringmann and Ken Ono},
  journal={Inventiones mathematicae},
In 1944, Freeman Dyson initiated the study of ranks of integer partitions. Here we solve the classical problem of obtaining formulas for Ne(n) (resp. No(n)), the number of partitions of n with even (resp. odd) rank. Thanks to Rademacher’s celebrated formula for the partition function, this problem is equivalent to that of obtaining a formula for the coefficients of the mock theta function f(q), a problem with its own long history dating to Ramanujan’s last letter to Hardy. Little was known… 
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