# THE f(q) MOCK THETA FUNCTION CONJECTURE AND PARTITION RANKS

@inproceedings{Ono2005THEFM, title={THE f(q) MOCK THETA FUNCTION CONJECTURE AND PARTITION RANKS}, author={Ken Ono}, year={2005} }

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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