Karl Mahlburg

Affiliation: MIT

Email: mahlburg@math.mit.edu

Title Of Talk: Asymptotics for crank and rank moments

Abstract: (Joint work with K. Bringmann and R. Rhoades). Dyson introduced his famous rank statistic for partitions in order to understand the Ramanujan congruences, and Garvan and Andrews later found the long-sought after crank to complete Dyson's challenge. A number of recent applications, such as Andrews' study of Durfee symbols and the smallest parts partition function, have relied on properties of the moments of the crank and rank functions. Garvan observed and conjectured that the crank moments are always larger than the rank moments. We prove a refined version of this conjecture by calculating the asymptotic main term for the difference of the crank and rank moments, and observe that it is always positive.

Last update made Mon Feb 2 14:05:16 EST 2009.
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