作者：Jendrej, Jacek; Lawrie, Andrew
作者单位：Sorbonne Universite; Universite Paris Cite; University System of Maryland; University of Maryland College Park
作者：Calegari, Frank; Dimitrov, Vesselin; Tang, Yunqing
作者单位：University of Chicago; California Institute of Technology; University of California System; University of California Berkeley
摘要：We prove the unbounded denominators conjecture in the theory of noncongruence modular forms for finite index subgroups of SL2(Z). Our result includes also Masons 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 second main theorem, the congruence subgro...
作者：Xu, Chenyang; Zhuang, Ziquan
作者单位：Princeton University; Johns Hopkins University
