PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, v.151, no.4, pp.1403 - 1414
Abstract
Let E be an elliptic curve over Q. Then, we show that the average analytic rank of E over cyclic extensions of degree l over Q with l a prime not equal to 2, is at most 2+rQ(E), where rQ(E) is the analytic rank of the elliptic curve E over Q. This bound is independent of the degree l Also, we also obtain some average analytic rank results over Sd-fields.