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Duality involving the mock theta function f ( q )
Author(s) -
Folsom Amanda,
Ono Ken
Publication year - 2008
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/jdm119
Subject(s) - ramanujan's sum , mathematics , modular form , pure mathematics , duality (order theory) , theta function , riemann zeta function , ramanujan theta function , kloosterman sum , holomorphic function , combinatorics
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.