Asymptotics for Rank and Crank Moments
نویسندگان
چکیده
Moments of the partition rank and crank statistics have been studied for their connections to combinatorial objects such as Durfee symbols, as well as for their connections to harmonic Maass forms. This paper proves a conjecture due to two of the authors that re ned a conjecture of Garvan. Garvan's original conjecture states that the moments of the crank function are always larger than the moments of the rank function, even though the moments have the same main asymptotic term. The re ned version provides precise asymptotic estimates for both the moments and their di erences. Our proof uses the Hardy-Ramanujan circle method, multiple sums of Bernoulli polynomials, and the theory of quasimock theta functions.
منابع مشابه
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