Class numbers of real quadratic fields

Abstract

Let d>0 be a fundamental discriminant of a real quadratic field. Let h(d) be the class number and εd the fundamental unit of the real quadratic field Q(d). In this paper, we prove that if there is an elliptic curve E over Q whose Hasse-Weil L-function LE/Q(s) has a zero of order g at s=1, then there is an effectively computable constant κ>0 satisfying [Formula presented] © 2020 Elsevier Inc.