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math.NT2025
The Ramanujan and Sato-Tate Conjectures for Bianchi modular forms
George Boxer, Frank Calegari, Toby Gee +2
We prove the Ramanujan and Sato-Tate conjectures for Bianchi modular forms of weight at least 2. More generally, we prove these conjectures for all regular algebraic cuspidal autom…
math.NT2024
The Unbounded Denominators Conjecture
Frank Calegari, Vesselin Dimitrov, Yunqing Tang
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 o…
math.NT2024
Cuspidal cohomology classes for GL_n(Z)
George Boxer, Frank Calegari, Toby Gee
We prove the existence of a cuspidal automorphic representation for of level one and weight zero. We construct using symmetric power functoriality an…