Document Type

Article

Publication Date

2008

Keywords

partition function, rank generating function, Maass form, weakly holomorphic modular form

Abstract

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

Publication Title

Acta Arithmetica

Volume

133

Issue

3

First Page

267

Last Page

279

DOI

10.4064/aa133-3-5

Required Publisher's Statement

c Instytut Matematyczny PAN, 2008

Free access to this article was provided by the Institute of Mathematics, Polish Academy of Sciences

Comments

Acta Arithmetica 133 (2008), 267-279MSC: Primary 11F37; Secondary 11P82.DOI: 10.4064/aa133-3-5

Subjects - Topical (LCSH)

Forms, Modular

Genre/Form

articles

Type

Text

Rights

Copying of this document in whole or in part is allowable only for scholarly purposes. It is understood, however, that any copying or publication of this document for commercial purposes, or for financial gain, shall not be allowed without the author’s written permission.

Language

English

Format

application/pdf

Download

Included in

Mathematics Commons

COinS