The Birch and Swinnerton-Dyer Conjecture

Joseph R. Keen

doi:10.5281/zenodo.19216423

March 25, 2026Open Access

The Birch and Swinnerton-Dyer Conjecture

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Key Points

The goal is to establish a proof of the Birch and Swinnerton-Dyer conjecture, linking elliptic curve properties to number theory.
Developed a mathematical proof addressing the conjecture's claims.
Analyzed the properties of elliptic curves and their L-functions.
Focused on the rank of elliptic curves related to the order of vanishing.
Demonstrated that the rank of an elliptic curve corresponds with the L-function's order of vanishing at s=1.

Abstract

Preprint v1 — A proof of the BSD conjecture relating the rank of an elliptic curve to the order of vanishing of its L-function at s=1. Abstract redacted pending IP review. Full abstract and unrestricted access will be available in v2 upon completion of intellectual property proceedings.

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Joseph R. Keen (2026) studied this question.

synapsesocial.com/papers/69c6207d15a0a509bde19030 https://doi.org/10.5281/zenodo.19216423

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The Birch and Swinnerton-Dyer Conjecture

Key Points

Abstract

Discussion

Cite This Study

The Birch and Swinnerton-Dyer Conjecture

Key Points

Abstract

Discussion

Cite This Study

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