The indicator of entire functions with rapidly oscillating coefficients

Let $f(z)=sum_{n=0}^infty c_nz^n$ be an entire function of order $rho_fin(0,+infty)$, let $sigma_f$ and $h_f(theta)$ be the type and the indicator of the function $f$, respectively, let $(p_n)$ be a sequence of positive integers with Hadamard gaps and $f_t(z)=sum_{n=0}^infty e^{ip_nt}c_nz^n$, where $tinmathbb{R}$. Then, for almost every $tinmathbb{R}$, the equality $h_{f_t}(theta)=sigma_f$ holds for every $thetainmathbb{R}$.