Numerical study of refined conjectures of the BSD type

2024/12/23 by Juan-Pablo Llerena-Córdova, Llerena-Córdova, Juan-Pablo
Engineering · Mathematics · #11Y40 (Primary) #Advanced Numerical Analysis Techniques #FOS: Mathematics #Mathematical Approximation and Integration #Mathematical functions and polynomials #Number Theory (math.NT) #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.2412.17703

openalex publication_date 2024/12/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In 1987, Mazur and Tate stated conjectures which, in some cases, resemble the classical Birch-Swinnerton-Dyer conjecture and its p-adic analog. We study experimentally three conjectures stated by Mazur and Tate using SageMath. Our findings indicate discrepancies in some of the original statements of some of the conjectures presented by Mazur and Tate. However, a slight modification on the statement of these conjectures does appear to hold.

Related

• Experimental Evidence on a Refined Conjecture of the BSD type
• On the refined `Birch--Swinnerton-Dyer type' conjectures of Mazur and Tate
• On pairs of p-adic analogues of the conjectures of Birch and Swinnerton-Dyer
• Recent progress on the Tate conjecture
• The Tate conjecture over finite fields (AIM talk)