Lower Bounds for Heights in Cyclotomic Extensions
نویسندگان
چکیده
We show that the height of a nonzero algebraic number α that lies in an abelian extension of the rationals and is not a root of unity must satisfy h(α) > 0.155097.
منابع مشابه
Karl 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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