Birch and Swinnerton-Dyer conjectureold and new

  1. Oscar Rivero-Salgado 1
  1. 1 Universitat Politècnica de Catalunya
    info

    Universitat Politècnica de Catalunya

    Barcelona, España

    ROR https://ror.org/03mb6wj31

Revista:
Reports@SCM: an electronic journal of the Societat Catalana de Matemàtiques

ISSN: 2385-4227

Ano de publicación: 2018

Volume: 4

Número: 1

Páxinas: 9-20

Tipo: Artigo

DIALNET GOOGLE SCHOLAR lock_openAcceso aberto editor

Outras publicacións en: Reports@SCM: an electronic journal of the Societat Catalana de Matemàtiques

Resumo

The Birch and Swinnerton-Dyer (BSD) conjecture is one of the millennium problems that has not been solved yet. Although it was formulated after different numerical experiments, there are several theoretical reasons and analogies with simpler mathematical objects that lead us to believe that it is true. We go through some of these analogies, and at the same time, we explain the most relevant results and generalizations that are currently known. At the end, we move to the rank two situation, recovering the elliptic Stark conjecture, closely related to BSD.Keywords: BSD, elliptic curve, L-series, modular forms, Gross-Zagier Stark conjecture.

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Fonte de datos: Dialnet