Displaying similar documents to “Binomial squares in pure cubic number fields”

Unit indices and cohomology for biquadratic extensions of imaginary quadratic fields

Marcin Mazur, Stephen V. Ullom (2008)

Journal de Théorie des Nombres de Bordeaux

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We investigate as Galois module the unit group of biquadratic extensions L / M of number fields. The 2 -rank of the first cohomology group of units of L / M is computed for general M . For M imaginary quadratic we determine a large portion of the cases (including all unramified L / M ) where the index [ V : V 1 V 2 V 3 ] takes its maximum value 8 , where V are units mod torsion of L and V i are units mod torsion of one of the 3 quadratic subfields of L / M .

Hasse’s problem for monogenic fields

Toru Nakahara (2009)

Annales mathématiques Blaise Pascal

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In this article we shall give a survey of Hasse’s problem for integral power bases of algebraic number fields during the last half of century. Specifically, we developed this problem for the abelian number fields and we shall show several substantial examples for our main theorem [] [], which will indicate the actual method to generalize for the forthcoming theme on Hasse’s problem [].

Non-trivial Ш in the Jacobian of an infinite family of curves of genus 2

Anna Arnth-Jensen, E. Victor Flynn (2009)

Journal de Théorie des Nombres de Bordeaux

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We give an infinite family of curves of genus 2 whose Jacobians have non-trivial members of the Tate-Shafarevich group for descent via Richelot isogeny. We prove this by performing a descent via Richelot isogeny and a complete 2-descent on the isogenous Jacobian. We also give an explicit model of an associated family of surfaces which violate the Hasse principle.

On D 5 -polynomials with integer coefficients

Yasuhiro Kishi (2009)

Annales mathématiques Blaise Pascal

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We give a family of D 5 -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.