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Open Problems in Mathematics pp 207–223Cite as

The Conjecture of Birch and Swinnerton-Dyer

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Abstract

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.

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Authors and Affiliations

  1. Emmanuel College, Cambridge, CB2 3AP, UK

    John Coates

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  1. John Coates
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Correspondence to John Coates .

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Editors and Affiliations

  1. Department of Mathematics, Senior Research Mathematician, Princeton University, Princeton, New Jersey, USA

    John Forbes Nash, Jr.

  2. Department of Mathematics, Princeton University, Princeton, New Jersey, USA

    Michael Th. Rassias

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Coates, J. (2016). The Conjecture of Birch and Swinnerton-Dyer. In: Nash, Jr., J., Rassias, M. (eds) Open Problems in Mathematics. Springer, Cham. https://doi.org/10.1007/978-3-319-32162-2_4

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