@article { , title = {Regularized inner products and errors of modularity}, abstract = {© The Author(s) 2016. We develop a regularization for Petersson inner products of arbitrary weakly holomorphic modular forms, generalizing several known regularizations. As one application, we extend work of Duke, Imamoglu, and Toth on regularized inner products of weakly holomorphic modular forms of weights 0 and 3/2. These regularized inner products can be evaluated in terms of the coefficients of holomorphic parts of harmonic Maass forms of dual weights. Moreover, we study the errors of modularity of the holomorphic parts of such a harmonic Maass forms and show that they induce cocyles in the first parabolic cohomology group introduced by Bruggeman, Choie, and the second author. This provides explicit representatives of the cohomology classes constructed abstractly and in a very general setting in their work.}, doi = {10.1093/imrn/rnw225}, eissn = {1687-0247}, issn = {1073-7928}, issue = {24}, journal = {International Mathematics Research Notices}, note = {Article not yet published in issue will need to add vol, issue no. and pagination. KJB 06.03.2017. Updated OL 19.01.2018. REF\_eligibility comment: Output can be accessed via a pre-print server, in accordance with REF OA requirements - please see ?https://arxiv.org/abs/1603.03056v2 . Version established to be accepted version deposited in?arXiv?21.09.2016 (i.e. same day as date of acceptance). SB, 07.01.20.}, pages = {7420-7458}, publicationstatus = {Published}, publisher = {Oxford University Press}, url = {https://nottingham-repository.worktribe.com/output/897783}, volume = {2017}, year = {2017}, author = {Bringmann, Kathrin and Diamantis, Nikolaos and Ehlen, Stephan} }