Birch and Swinnerton-Dyer conjecture: old and new

Autors/ores

  • Oscar Rivero-Salgado Universitat Politècnica de Catalunya

Paraules clau:

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

Resum

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.

Descàrregues

Les dades de descàrrega encara no estan disponibles.

Biografia de l'autor/a

Oscar Rivero-Salgado, Universitat Politècnica de Catalunya



Descàrregues

Com citar

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

Número

Vol. 4 Núm. 1 (2018)

Secció

Articles

Llicència

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