Poincaré series and the divisors of modular forms

Choi, D.

doi:10.1090/S0002-9939-2010-10133-8

Poincaré series and the divisors of modular forms
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Proc. Amer. Math. Soc. 138 (2010), 3393-3403 Request permission

Abstract:

Recently, Bruinier, Kohnen and Ono obtained an explicit description of the action of the theta-operator on meromorphic modular forms $f$ on $SL_2(\mathbb {Z})$ in terms of the values of modular functions at points in the divisor of $f$. Using this result, they studied the exponents in the infinite product expansion of a modular form and recurrence relations for Fourier coefficients of a modular form. In this paper, we extend these results to meromorphic modular forms on $\Gamma _0(N)$ for an arbitrary positive integer $N>1$.

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