Divisibility of Class Numbers of Imaginary Quadratic Fields

Let d be a square-free number and let CL(−d) denote the ideal class group of the imaginary quadratic number field Q(√−d). Further let h(−d) = #CL(−d) denote the class number. For integers g ⩾ 2, we define Ng(X) to be the number of square-free d ⩾ X such that CL(−d) contains an element of order g. Gauss' genus theory demonstrates that if d has at least two odd prime factors (in particular, for almost all d) then CL(−d) contains Z2 as a subgroup....