The dimensions of spaces of holomorphic second-order automorphic forms and their cohomology
Nikolaos Diamantis, Cormac O'Sullivan
Abstract
Second-order automorphic forms are similar to the usual automorphic forms but have a weaker automorphy condition. We answer a question of Zagier and find the dimensions of spaces of holomorphic, even weight, second-order forms. We also establish a cohomological interpretation.
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