- partition function,
- rank generating function,
- Maass form,
- weakly holomorphic modular form
Introduction and statement of results. Recent works have illustrated that the Fourier coefficients of harmonic weak Maass forms of weight 1/2 contain a wealth of number-theoretic and combinatorial information. After these works, it is known that many enigmatic q-series (the “mock theta functions” of Ramanujan, and certain rank-generating functions from the theory of partitions, for example) arise naturally as the “holomorphic parts” of such forms. See, for example, Bringmann and Ono [5, 6], Bringmann, Ono, and Rhoades [7], Zwegers [19], Bringmann and Lovejoy [4], Lovejoy and Osburn [12], or see the survey paper [13] for an overview. As another striking example, Bruinier and Ono [9] show that the coefficients of the holomorphic parts of weight 1/2 Maass forms determine the fields of definition of certain Heegner divisors in the Jacobians of modular curves, which in turn determine the vanishing or non-vanishing of derivatives of modular L-functions
Acta Arithmetica 133 (2008), 267-279MSC: Primary 11F37; Secondary 11P82.DOI: 10.4064/aa133-3-5
Available at: http://works.bepress.com/stephanie-treneer/12/
Acta Arithmetica 133 (2008), 267-279MSC: Primary 11F37; Secondary 11P82.DOI: 10.4064/aa133-3-5