Abstract
For a positive integer N divisible by 4, 5, 6, 7 or 9, let \(\mathcal {O}_{1,N}(\mathbb {Q})\) be the ring of weakly holomorphic modular functions for the congruence subgroup \(\Gamma _1(N)\) with rational Fourier coefficients. We present explicit generators of the ring \(\mathcal {O}_{1,N}(\mathbb {Q})\) over \(\mathbb {Q}\) by making use of modular units which have infinite product expansions.
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Koo, J.K., Yoon, D.S. Generators of the ring of weakly holomorphic modular functions for \(\Gamma _1(N)\) . Ramanujan J 42, 583–599 (2017). https://doi.org/10.1007/s11139-015-9742-4
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DOI: https://doi.org/10.1007/s11139-015-9742-4