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Harmonic Maass Forms and Mock Modular Forms - Theory and Applications (Hardcover)
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Harmonic Maass Forms and Mock Modular Forms - Theory and Applications (Hardcover)
Series: Colloquium Publications
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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.
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