MATH Seminar

Title: Eichler-Shimura theory for mock modular forms
Seminar: Number Theory
Speaker: Zachary Kent of Emory University
Contact: Ken Ono, ono@mathcs.emory.edu
Date: 2010-08-24 at 3:00PM
Venue: MSC E408
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Abstract: We use mock modular forms to compute generating functions for the critical values of modular L-functions, and we answer a generalized form of a question of Kohnen and Zagier by deriving the ``extra relation" that is satised by even periods of weakly holomorphic cusp forms. To obtain these results we derive an Eichler-Shimura theory for weakly holomorphic modular forms and mock modular forms. This includes two ``Eichler-Shimura isomorphisms", a ``multiplicity two" Hecke theory, a correspondence between mock modular periods and classical periods, and a ``Haberland-type" formula which expresses Petersson's inner product and a related antisymmetric inner product on weakly holomorphic modular forms in terms of periods.