Mock period functions, sesquiharmonic Maass forms, and non-critical values of L-functions

作者：Bringmann Kathrin^*; Diamantis Nikolaos; Raum Martin

来源：Advances in Mathematics, 2013, 233(1): 115-134.

DOI：10.1016/j.aim.2012.09.025

• Period polynomials
• Mock period polynomials
• Mock modular forms
• Sesquiharmonic Maass forms
• Noncritical L-values

We introduce a new technique of completion for 1-cohomology which parallels the corresponding technique in the theory of mock modular forms. This technique is applied in the context of non-critical values of L-functions of GL(2) cusp forms. We prove that a generating series of non-critical values can be interpreted as a mock period function we define in analogy with period polynomials. Further, we prove that non-critical values can be encoded into a sesquiharmonic Maass form. Finally, we formulate and prove an Eichler-Shimura-type isomorphism for the space of mock period functions.

• 出版日期2013-1-30