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Questions about modular forms and related areas

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Decomposition of a sum of holomorphic squares into modular forms

Say there is a (non-holomorphic) real function $Z(\tau,\bar{\tau})$ which obeys the (non-holomorphic) modularity conditions of some weight $k$ $$Z(\tau+1,\bar{\tau}+1)=Z(\tau,\bar{\tau}),\qquad Z(-1/\ …
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