Resumen de Poincaré series and the divisors of modular forms

D. Choi

• Recently, Bruinier, Kohnen and Ono obtained an explicit description of the action of the theta-operator on meromorphic modular forms on in terms of the values of modular functions at points in the divisor of . 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 for an arbitrary positive integer .