منابع مشابه
O ct 2 00 8 Kummer Generators and Lambda Invariants
Let F0 = Q(√ −d) be an imaginary quadratic field with 3 ∤ d and let K0 = Q(√ 3d). Let ε0 be the fundamental unit of K0 and let λ be the Iwasawa λ-invariant for the cyclotomic Z3-extension of F0. The theory of 3-adic L-functions gives conditions for λ ≥ 2 in terms of ǫ0 and the class numbers of F0 and K0. We construct units of K1, the first level of the Z3-extension of K0, that potentially occur...
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Let L ⊆ C be a lattice and consider the compact complex torus XL = C/L. Let Γ 6 Aut(L) ∩ SL2m C be a (finite) group of automorphisms of L whose action on C is semifree (i.e., free away from 0). X L consists of finitely many isolated fixed points, so the orbifold XL/Γ has finitely many isolated singularities. We can resolve these singularities by ‘blowing up’ each of the singular points. In fact...
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Let K = Q( √ −d) be an imaginary quadratic field and let Q( √ 3d) be the associated real quadratic field. Starting from the Cohen-Lenstra heuristics and Scholz’s theorem, we make predictions for the behaviors of the 3-parts of the class groups of these two fields as d varies. We deduce heuristic predictions for the behavior of the Iwasawa λ-invariant for the cyclotomic Z3extension of K and test...
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ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 2010
ISSN: 0022-314X
DOI: 10.1016/j.jnt.2009.06.001