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 f on SL 2(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 Γ0(N) for an arbitrary positive integer N >1.
Proceedings of the American Mathematical Society
https://doi.org/10.1090/S0002-9939-2010-10133-8
Mathematics(all)
10.1090/S0002-9939-2010-10133-8
Dive into the research topics of 'Poincaré series and the divisors of modular forms'. Together they form a unique fingerprint.
Modular Forms Mathematics 100%
Divisor Mathematics 85%
Series Mathematics 58%
Meromorphic Mathematics 51%
Modular Functions Mathematics 30%
Infinite product Mathematics 27%
Fourier coefficients Mathematics 24%
Recurrence relation Mathematics 23%
Choi, D. (2010). Poincaré series and the divisors of modular forms. Proceedings of the American Mathematical Society, 138(10), 3393-3403. https://doi.org/10.1090/S0002-9939-2010-10133-8
Poincaré series and the divisors of modular forms. / Choi, D.
In: Proceedings of the American Mathematical Society, Vol. 138, No. 10, 10.2010, p. 3393-3403.
Choi, D 2010, 'Poincaré series and the divisors of modular forms', Proceedings of the American Mathematical Society, vol. 138, no. 10, pp. 3393-3403. https://doi.org/10.1090/S0002-9939-2010-10133-8
Choi D. Poincaré series and the divisors of modular forms. Proceedings of the American Mathematical Society. 2010 Oct;138(10):3393-3403. https://doi.org/10.1090/S0002-9939-2010-10133-8
Choi, D. / Poincaré series and the divisors of modular forms. In: Proceedings of the American Mathematical Society. 2010 ; Vol. 138, No. 10. pp. 3393-3403.
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title = "Poincar{\'e} series and the divisors of modular forms",
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(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 Γ0(N) for an arbitrary positive integer N >1.",
author = "D. Choi",
doi = "10.1090/S0002-9939-2010-10133-8",
journal = "Proceedings of the American Mathematical Society",
publisher = "American Mathematical Society",
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AU - Choi, D.
N2 - Recently, Bruinier, Kohnen and Ono obtained an explicit description of the action of the theta-operator on meromorphic modular forms f on SL 2(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 Γ0(N) for an arbitrary positive integer N >1.
AB - Recently, Bruinier, Kohnen and Ono obtained an explicit description of the action of the theta-operator on meromorphic modular forms f on SL 2(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 Γ0(N) for an arbitrary positive integer N >1.
U2 - 10.1090/S0002-9939-2010-10133-8
DO - 10.1090/S0002-9939-2010-10133-8
JO - Proceedings of the American Mathematical Society
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