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The Bloch-Kato conjecture on special values of L -functions. A survey of known results

Guido Kings (2003)

Journal de théorie des nombres de Bordeaux

This paper contains an overview of the known cases of the Bloch-Kato conjecture. It does not attempt to overview the known cases of the Beilinson conjecture and also excludes the Birch and Swinnerton-Dyer point. The paper starts with a brief review of the formulation of the general conjecture. The final part gives a brief sketch of the proofs in the known cases.

Topics in computational algebraic number theory

Karim Belabas (2004)

Journal de Théorie des Nombres de Bordeaux

We describe practical algorithms from computational algebraic number theory, with applications to class field theory. These include basic arithmetic, approximation and uniformizers, discrete logarithms and computation of class fields. All algorithms have been implemented in the Pari/Gp system.

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