Elliptic Curves of High Rank and the Riemann Zeta Function on the One Line

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 in which the zeta function on the one line plays a prominent role.

2000 AMS Subject Classification::

• 11M41

Keywords:

• L-functions
• rank

Notes

¹Available at http://www.lmfdb.org/EllipticCurve/Q.

²The author's L-function package is available at http://code.google.com/p/l-calc .

³PARI is available at http://pari.math.u-bordeaux.fr .