Moments of the Critical Values of Families of Elliptic Curves, with Applications

@article{Young2007MomentsOT,
title={Moments of the Critical Values of Families of Elliptic Curves, with Applications},
author={M. Young},
journal={Canadian Journal of Mathematics},
year={2007},
volume={62},
pages={1155-1181}
}

We make conjectures on the moments of the central values of the family of all elliptic curves and on the moments of the first derivative of the central values of a large family of positive rank curves. In both cases the order of magnitude is the same as that of the moments of the central values of an orthogonal family of L-functions. Notably, we predict that the critical values of all rank 1 elliptic curves is logarithmically larger than the rank 1 curves in the positive rank family… CONTINUE READING