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Harmonic Maass Forms and Mock Modular Forms.

Author: Kathrin Bringmann; Amanda Folsom; Ken Ono
Publisher: Providence : American Mathematical Society, 2017.
Series: Colloquium Publications.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
Modular forms and Jacobi forms play a central role in many areas of mathematics. Over the last 10-15 years, this theory has been extended to certain non-holomorphic functions, the so-called "harmonic Maass forms". The first glimpses of this theory appeared in Ramanujan's enigmatic last letter to G.H. Hardy written from his deathbed. Ramanujan discovered functions he called "mock theta functions" which over eighty  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Bringmann, Kathrin.
Harmonic Maass Forms and Mock Modular Forms: Theory and Applications.
Providence : American Mathematical Society, ©2017
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Kathrin Bringmann; Amanda Folsom; Ken Ono
ISBN: 9781470443139 1470443139
OCLC Number: 1018235766
Description: 1 online resource (409 pages).
Contents: Background: Elliptic functionsTheta functions and holomorphic Jacobi formsClassical Maass formsHarmonic Maass forms and mock modular forms: The basicsDifferential operators and mock modular formsExamples of harmonic Maass formsHecke theoryZwegers' thesisRamanujan's mock theta functionsHolomorphic projectionMeromorhic Jacobi formsMock modular Eichler-shimura theoryRelated automorphic formsApplications: Partitions and unimodal sequencesAsymptotics for coefficients of modular-type functionsHarmonic Maass forms as arithmetic and geometric generating functionsShifted convolution $L$-functionsGeneralized Borcherds productsElliptic curves over $\mathbb{Q}$Representation theory and mock modular formsQuantum modular formsRepresentations of mock theta functionsBibliographyIndex
Series Title: Colloquium Publications.

Abstract:

Modular forms and Jacobi forms play a central role in many areas of mathematics. In recent years, this theory has been extended to certain non-holomorphic functions, the so-called "harmonic Maass  Read more...

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