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Poincaré series and the divisors of modular forms

Author: D. Choi
Journal: Proc. Amer. Math. Soc. 138 (2010), 3393-3403
MSC (2010): Primary 11F12; Secondary 11F30
Published electronically: June 3, 2010
MathSciNet review: 2661540
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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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Additional Information

D. Choi
Affiliation: School of Liberal Arts and Sciences, Korea Aerospace University, 200-1, Hwajeon-dong, Goyang, Gyeonggi 412-791, Korea

Keywords: Borcherds exponents, Poincar\'{e} series, divisors of modular forms
Received by editor(s): April 2, 2009
Received by editor(s) in revised form: July 27, 2009
Published electronically: June 3, 2010
Communicated by: Ken Ono
Article copyright: © Copyright 2010 American Mathematical Society

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