Duality involving the mock theta function f(q)

• Autores: Amanda Folsom
• Localización: Journal of the London Mathematical Society, ISSN 0024-6107, Vol. 77, Nº 2, 2008, págs. 320-334
• Idioma: inglés
• DOI: 10.1112/jlms/jdm119
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• Resumen

  • We show that the coefficients of Ramanujan's mock theta function f(q) are the first non-trivial coefficients of a canonical sequence of modular forms. This fact follows from a duality which equates coefficients of the holomorphic projections of certain weight 1/2 Maass forms with coefficients of certain weight 3/2 modular forms. This work depends on the theory of Poincaré series, and a modification of an argument of Goldfeld and Sarnak on Kloosterman�Selberg zeta functions.