On the distribution of analytic ranks of elliptic curves

• Published in: Mathematische Zeitschrift Vol. 305; no. 3
• Main Authors: Cho, Peter J., Jeong, Keunyoung
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.11.2023; Springer Nature B.V
• Subjects: Curves; Mathematical analysis; Mathematics; Mathematics and Statistics; Upper bounds; Secondary 11G40; Primary 11G05; Trace formula; 11M26; Rank; Elliptic curve; GRH; BSD conjecture

In this paper, under GRH for elliptic curve L -functions, we give an upper bound for the probability for an elliptic curve with analytic rank ≤ a for a ≥ 11 , and also provide an upper bound of n -th moments of analytic ranks of elliptic curves. These are applications of counting elliptic curves wit...