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Harmonic Maass Forms and Mock Modular Forms(Colloquium Publications Vol. 64) hardcover 391 p. 18

Bringmann, Kathrin, Folsom, Amanda, Ono, Ken, Rolen, Larry 　著

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発行年月	2017年12月
出版社／提供元	American Mathematical Society
出版国	アメリカ合衆国
言語	英語
媒体	冊子
装丁	hardcover
ページ数／巻数	391 p.
ジャンル	洋書
ISBN	9781470419448
商品コード	1026516145
本の性格	学術書
新刊案内掲載月	2018年01月
商品URL	https://kw.maruzen.co.jp/ims/itemDetail.html?itmCd=1026516145

内容

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.

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

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