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2016•American journal of mathematics and statisticsOpen access

Review of the Birch and Swinnerton-Dyer Conjecture

R. K. Ansah, Richard Kena Boadi, William Obeng–Denteh, Akoto Yaw Omari-Sasu

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Abstract

The Birch and Swinnerton-Dyer Conjecture is a well known mathematics problem in the area of Elliptic Curve. One of the crowning moments is the paper by Andrew Wiles which is difficult to understand let alone to appreciate the conjecture. This paper surveys the background of the conjecture treating the ranks of the elliptic curves over the field of rational numbers. Then we present major results like the theorems of Mordell and Mazur leading us to the current state of the conjecture.

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What this paper is about

The Birch and Swinnerton-Dyer Conjecture is a well known mathematics problem in the area of Elliptic Curve. One of the crowning moments is the paper by Andrew Wiles which is difficult to understand let alone to appreciate the conjecture. This paper surveys the background of the conjecture treating the ranks of the elliptic curves over the field of rational numbers. Then we present major results like the theorems of Mordell and Mazur leading us to the current state of the conjecture.

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Available abstract

The Birch and Swinnerton-Dyer Conjecture is a well known mathematics problem in the area of Elliptic Curve. One of the crowning moments is the paper by Andrew Wiles which is difficult to understand let alone to appreciate the conjecture. This paper surveys the background of the conjecture treating the ranks of the elliptic curves over the field of rational numbers. Then we present major results like the theorems of Mordell and Mazur leading us to the current state of the conjecture.

Key concepts: Conjecture, Mathematics, Elliptic curve, Pure mathematics, Combinatorics

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