期刊名称：Proceedings of the National Academy of Sciences
印刷版ISSN：0027-8424
电子版ISSN：1091-6490
出版年度：2010
卷号：107
期号：14
页码：6169-6174
DOI：10.1073/pnas.1001355107
语种：English
出版社：The National Academy of Sciences of the United States of America
摘要：A "mock modular form" is the holomorphic part of a harmonic Maass form f. The nonholomorphic part of f is a period integral of its "shadow," a cusp form g. A direct method for relating the coefficients of shadows and mock modular forms is not known. We solve these problems when the shadow is an integer weight newform. Our solution is p-adic, and it relies on our definition of an algebraic "regularized mock modular form." As an application, we consider the modular solution to the cubic "arithmetic-geometric mean."
