14 citations · 31 across the 14 of their papers we have counts for
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math.NT2004★ 4 cited
Irrationality of certain p-adic periods for small p
Frank Calegari
Following Apery's proof of the irrationality of zeta(3), Beukers found an elegant reinterpretation of Apery's arguments using modular forms. We show how Beukers arguments can be ad…
math.NT2004
Eisenstein Deformation Rings
Frank Calegari
We prove R = T theorems for certain reducible residual Galois representations. We answer in the positive a question of Gross and Lubin on whether certain Hecke algebras T are discr…
math.NT2004
Mod p representations on elliptic curves
Frank Calegari
Modular Galois representations into GL_2(F_p) with cyclotomic determinant arise from elliptic curves for p = 2,3,5. We show (by constructing explicit examples) that such elliptic c…