The average analytic rank of elliptic curves

Details The average analytic rank of elliptic curves The average analytic rank of elliptic curves

2003-05-07

arxiv.org/abs/math/0305114v1

Mathematics

Number Theory

28 pages

Scientific paper

All the results in this paper are conditional on the Riemann Hypothesis for the L-functions of elliptic curves. Under this assumption, we show that the average analytic rank of all elliptic curves over Q is at most 2, thereby improving a result of Brumer. We also show that the average within any family of quadratic twists is at most 3/2, improving a result of Goldfeld. A third result concerns the density of curves with analytic rank at least R, and shows that the proportion of such curves decreases faster than exponentially as R grows. The proofs depend on an analogue of Weil's ``explicit formula''.

Affiliated with

Also associated with

No associations

Rating

The average analytic rank of elliptic curves does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with The average analytic rank of elliptic curves, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The average analytic rank of elliptic curves will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-23491