The Conjecture of Birch and Swinnerton-Dyer

  • John CoatesEmail author


The conjecture of Birch and Swinnerton-Dyer is one of the principal open problems of number theory today. Since it involves exact formulae rather than asymptotic questions, it has been tested numerically more extensively than any other conjecture in the history of number theory, and the numerical results obtained have always been in perfect accord with every aspect of the conjecture. The present article is aimed at the non-expert, and gives a brief account of the history of the conjecture, its precise formulation, and the partial results obtained so far in support of it.


Elliptic Curve Elliptic Curf Abelian Variety Euler System Euler Product 
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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Emmanuel CollegeCambridgeUK

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