A mean value theorem for cubic fields Original Research Article

Let r(n) denote the number of integral ideals of norm n in a cubic extension K of the rationals, and define S(x)= ∑nless-than-or-equals, slantxr(n) and Δ(x)=S(x)−αx where α is the residue of the Dedekind zeta function ζ(s,K) at 1. It is shown that the abscissa of convergence ofimageis image as expected.