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arXiv · 2311.07641

A visual perspective on the Birch and Swinnerton-Dyer conjecture through a family of approximations of $L$-functions

Maria Nastasescu·Bogdan Stoica·Alexandru Zaharescu
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Abstract

We investigate the properties of a family of approximations of the Hasse-Weil $L$-function associated to an elliptic curve $E$ over $\mathbb{Q}$. We give a precise expression for the error of the approximations, and provide a visual interpretation of the analytic rank $m$ of $E$ as a sequence of near regular polygons around the center of the critical strip, each with vertices at the zeros of the approximations.

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Maria Nastasescu, Bogdan Stoica, Alexandru Zaharescu. 2023-11-13. A visual perspective on the Birch and Swinnerton-Dyer conjecture through a family of approximations of $L$-functions. https://arxiv.org/abs/2311.07641

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