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Locally harmonic Maass forms of positive even weight

Locally harmonic Maass forms of positive even weight

Abstract We twist Zagier’s function f k,D by a sign function and a genus character. Assuming weight 0 < k ≡ 2 (mod 4), and letting D be a positive non-square discriminant, we prove that the obstruction to modularity caused by the sign function can be corrected obtaining a locally …