On the distribution of analytic ranks of elliptic curves

2020/03/20 by Cho, Peter J., Jeong, Keunyoung
#11G05 #11G40 #11M26 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2003.09102

Abstract

In this paper, under GRH for elliptic L-functions, we give an upper bound for the probability for an elliptic curve with analytic rank ≤ a for a ≥ 11, and also give an upper bound of n-th moments of analytic ranks of elliptic curves. These are applications of counting elliptic curves with local conditions, for example, having good reduction at p.

Related

• The average analytic rank of elliptic curves
• Upper bounds for moments of analytic ranks of elliptic curves over number fields
• Quantitative rank distribution conjecture over \mathbbF_q(t)
• Moments of the rank of elliptic curves
• The Parity of Analytic Ranks among Quadratic Twists of Elliptic Curves over Number Fields