Birch and Swinnerton-Dyer conjecture: old and new

Authors

  • Oscar Rivero-Salgado Universitat Politècnica de Catalunya

Keywords:

BSD, elliptic curve, L-series, modular forms, Gross-Zagier Stark conjecture.

Abstract

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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Author Biography

Oscar Rivero-Salgado, Universitat Politècnica de Catalunya



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How to Cite

Rivero-Salgado, O. (2019). Birch and Swinnerton-Dyer conjecture: old and new. Reports@SCM, 4(1), 9–20. Retrieved from https://revistes.iec.cat/index.php/reports/article/view/145798

Issue

Vol. 4 No. 1 (2018)

Section

Articles

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