Elliptic units of cyclic unramified extensions of complex quadratic fields
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Computations of elliptic units for real quadratic fields
Elliptic units, which are obtained by evaluating modular units at quadratic imaginary arguments of the Poincaré upper half-plane, allow the analytic construction of abelian extensions of imaginary quadratic fields. The Kronecker limit formula relates the complex absolute values of these units to values of zeta functions, and allowed Stark to prove his rank one archimedean conjecture for abelian...
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We give a family of D5-polynomials with integer coefficients whose splitting fields over Q are unramified cyclic quintic extensions of quadratic fields. Our polynomials are constructed by using Fibonacci, Lucas numbers and units of certain cyclic quartic fields.
متن کاملKarl Rubin Henri Darmon September 9 , 2007
1. Thaine’s “purely cyclotomic” method [Th88] for bounding the exponents of the ideal class groups of cyclotomic fields. The bounds that Thaine obtained were already known thanks to the proof of the Main Conjecture by Mazur andWiles, in which unramified abelian extensions of cyclotomic fields were constructed from reducible two-dimensional Galois representations occuring in the Jacobians of mod...
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The first mathematician who studied quaternion extensions (H8-extensions for short) was Dedekind [6]; he gave Q( √ (2 + √ 2)(3 + √ 6) ) as an example. The question whether given quadratic or biquadratic number fields can be embedded in a quaternion extension was extensively studied by Rosenblüth [32], Reichardt [31], Witt [36], and Damey and Martinet [5]; see Ledet [19] and the surveys [15] and...
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We exhibit, for each n ≥ 5, infinitely many quadratic number fields admitting unramified degree n extensions with prescribed signature whose normal closures have Galois group An. This generalizes a result of Uchida and Yamamoto, which did not include the ability to restrict the signature, and a result of Yamamura, which was the case n = 5. It is a folk conjecture that for n ≥ 5, all but finitel...
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تاریخ انتشار 2006