Asymptotic behavior of the number of representations of large integers by certain positive-definite ternary quadratic forms

Continuing the work in an earlier paper, the author uses an assumption concerning the location of zeros of Dirichlet $L$-series in order to derive an asymptotic formula for the number of representations of large integers by the ternary form $f(x,y,z)=x^2+2y^2+Dz^2$, where $D$ is of the form $x^2+2y^2$.