Harmonic Maass Forms and Mock Modular Forms
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Harmonic Maass Forms and Mock Modular Forms: Theory and Applications(Colloquium Publications)

Harmonic Maass Forms and Mock Modular Forms: Theory and Applications(Colloquium Publications)


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About the Book

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 years later were recognized as pieces of harmonic Maass forms. This book contains the essential features of the theory of harmonic Maass forms and mock modular forms, together with a wide variety of applications to algebraic number theory, combinatorics, elliptic curves, mathematical physics, quantum modular forms, and representation theory.

Table of Contents:
Background: Elliptic functions Theta functions and holomorphic Jacobi forms Classical Maass forms Harmonic Maass forms and mock modular forms: The basics Differential operators and mock modular forms Examples of harmonic Maass forms Hecke theory Zwegers' thesis Ramanujan's mock theta functions Holomorphic projection Meromorhic Jacobi forms Mock modular Eichler-shimura theory Related automorphic forms Applications: Partitions and unimodal sequences Asymptotics for coefficients of modular-type functions Harmonic Maass forms as arithmetic and geometric generating functions Shifted convolution $L$-functions Generalized Borcherds products Elliptic curves over $\mathbb{Q}$ Representation theory and mock modular forms Quantum modular forms Representations of mock theta functions Bibliography Index

About the Author :
Kathrin Bringmann, University of Cologne, Germany. Amanda Folsom, Amherst College, MA. Ken Ono, Emory University, Atlanta, GA. Larry Rolen, Trinity College, Dublin, Ireland.

Review :
This wonderful book is very exciting to me as it presents some very exotic and beautiful stuff that I, for one, had no notion of...I'm happy to be enlightened, if only in a preliminary way. But this book is tailor-made to lead wayward sons like me back home and to light the right kind of fire under us...Excellent." — Michael Berg, MAA Reviews


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Product Details
  • ISBN-13: 9781470419448
  • Publisher: American Mathematical Society
  • Publisher Imprint: American Mathematical Society
  • Height: 254 mm
  • No of Pages: 391
  • Sub Title: Theory and Applications
  • Width: 178 mm
  • ISBN-10: 1470419440
  • Publisher Date: 30 Dec 2017
  • Binding: Hardback
  • Language: English
  • Series Title: Colloquium Publications
  • Weight: 825 gr


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