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By using the Schur test, we give some upper and lower estimates on the normof a composition operator on $\mathcal{H}^2$, the space of Dirichlet serieswith square summable coefficients, for the inducing symbol$\varphi(s)=c_1+c_{q}q^{-s}$ where $q\geq 2$ is a fixed integer. We also givean estimate on the approximation numbers of such an operator.

Estimate for norm of a composition operator on the Hardy-Dirichlet space