Elliptic curves of high rank and the Riemann zeta function on the one line

TL;DR

This paper explores the relationship between elliptic curves of high rank and the Riemann zeta function on the critical line, supported by experimental data and statistical analysis of L-functions.

Contribution

It presents experimental evidence and discusses statistical properties linking high-rank elliptic curves to the behavior of the Riemann zeta function on the one line.

Findings

Experimental connection between high-rank elliptic curves and zeta function behavior

Statistics involving L-functions highlight the role of the zeta function on the critical line

Discussion of potential implications for number theory

Abstract

We describe some experiments that show a connection between elliptic curves of high rank and the Riemann zeta function on the one line. We also discuss a couple of statistics involving $L$-functions where the zeta function on the one line plays a prominent role.