
Date : 20220506 (Fri) 16:00

Place : 27325 (SNU)
 Speaker : Keunyoung Jeong (Chonnam National University)
 Title : On an upper bound of the average analytic rank of a family of elliptic curves
 Abstract; The average of the rank of elliptic curves over rational numbers in a ``natural'' family is expected to be 1/2. For example, Goldfeld conjectured that the average of analytic ranks of the quadratic twist family of an elliptic curve over rational numbers is 1/2. In this talk, we will introduce machinery which gives an upper bound of the average of analytic ranks of a family of elliptic curves. To run the machinery, we need to know the probability that an elliptic curve in the family has good/multiplicative/additive reduction (actually we need something more) and use trace formulas. Using the machinery on the set of all elliptic curves over rationals and the set of elliptic curves with a given torsion subgroup respectively, we can compute an upper bound of the nth moment of the average. This is the first result on an upper bound of the average of the family of elliptic curves with a fixed torsion group, as far as we know. This is joint work with Peter J. Cho.
 Website: https://sites.google.com/view/snunt/seminars