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

@article{Bringmann2006TheFM,
title={The f(q) mock theta function conjecture and partition ranks},
author={Kathrin Bringmann and Ken Ono},
journal={Inventiones mathematicae},
year={2006},
volume={165},
pages={243-266}
}
• Published 31 January 2006
• Mathematics
• 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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