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math.NT2024★ 1 cited
The adelic closure of triangle groups
Frank Calegari
Motivated by questions arising from billiard trajectories in the regular -gon, McMullen defined a pair of functions and on the cusps of the corresponding triangle gr…
math.NT2009
Even Galois Representations and the Fontaine-Mazur Conjecture
Frank Calegari
We prove some cases of the Fontaine-Mazur conjecture for even Galois representations. In particular, we prove, under mild hypotheses, that there are no irreducible two-dimensional…
math.NT2004
Conjectures about discriminants of Hecke algebras at prime level
Frank Calegari, William Stein
We study p-divisibility of discriminants of Hecke algebras associated to spaces of cusp forms of prime level. We make a precise conjecture about the indexes of Hecke algebras in th…