Year: 2022
Type: article
Abstract: Let E E be an elliptic curve over Q \mathbb {Q} with discriminant Δ E \Delta _E . For primes p p of good reduction, let N p N_p be the number of points modulo p p and write N p = p + 1 − a p N_p=p+1-a_p . In 1965, Birch and Swinnerton-Dyer formulated a conjecture which implies lim x → ∞ 1 log x ∑ p ≤ x p ∤ Δ E a p log p p = − r + 1 2 , \begin{equation*} \lim _{x\to \infty }\frac {1}{\log x}\sum _{\substack {p\leq x\\ p\nmid \Delta _{E
Source: Mathematics of Computation
DOI: 10.1090/mcom/3773
Authors: Seoyoung Kim, M. Murty
Institution: Queen's University
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Awards: G1986352324, G570963412
OpenAlex ID: W4295631274