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.

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.

Reviews
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



Book Information
ISBN 9781470479848
Author Kathrin Bringmann
Format Paperback
Page Count 391
Imprint American Mathematical Society
Publisher American Mathematical Society