Lifting Elliptic Cusp Forms to Maass Forms with an Application to Partitions
نویسندگان
چکیده
Abstract. For 2 < k ∈ 1 2 Z, we define lifts of cuspidal Poincaré series in Sk(Γ0(N)) to weight 2 − k harmonic weak Maass forms. This construction answers a question of Dyson by providing the general framework “explaining” Ramanujan’s mock theta functions. As an application, we show that the number of partitions of a positive integer n is the “trace” of singular moduli of a Maass form arising from the lift of a weight 4 cusp form corresponding to a Calabi-Yau threefold.
منابع مشابه
Lifting cusp forms to Maass forms with an application to partitions.
For 2 < k [abstract: see text] we define lifts of cuspidal Poincaré series in S(k)(Gamma(0)(N)) to weight 2 - k harmonic weak Maass forms. This construction answers a question of Dyson by providing the general framework "explaining" Ramanujan's mock theta functions. As an application, we show that the number of partitions of a positive integer n is the "trace" of singular moduli of a Maass form...
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تاریخ انتشار 2006