Upper bounds for moments of analytic ranks of elliptic curves over number fields

2026/07/17 by Tristan Phillips, Saahil Sharma
Mathematics · #math.NT

paper · pdf

Abstract

We prove a conditional upper bound for moments of the analytic rank of elliptic curves over number fields. We also prove conditional bounds for the density of elliptic curves with analytic rank larger than a given bound.

Related

• On the distribution of analytic ranks of elliptic curves
• Conditionally bounding analytic ranks of elliptic curves
• Analytic ranks of elliptic curves over number fields
• Moments of the rank of elliptic curves
• The Parity of Analytic Ranks among Quadratic Twists of Elliptic Curves over Number Fields