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- W3200461275 abstract "We prove the unbounded denominators conjecture in the theory of noncongruence modular forms for finite index subgroups of SL_2(Z). Our result includes also Mason's generalization of the original conjecture to the setting of vector-valued modular forms, thereby supplying a new path to the congruence property in rational conformal field theory. The proof involves a new arithmetic holonomicity bound of a potential-theoretic flavor, together with Nevanlinna's second main theorem, the congruence subgroup property of SL_2(Z[1/p]), and a close description of the Fuchsian uniformization D(0,1)/Gamma_N of the Riemann surface C setminus mu_N." @default.
- W3200461275 created "2021-09-27" @default.
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- W3200461275 date "2021-09-18" @default.
- W3200461275 modified "2023-10-17" @default.
- W3200461275 title "The Unbounded Denominators Conjecture" @default.
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- W3200461275 doi "https://doi.org/10.48550/arxiv.2109.09040" @default.
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