Obtain a closed norm formula for general finite-prime composition symbols

Derive a closed formula for the operator norm of a composition operator induced by a general finite-prime, zero-characteristic Dirichlet-series symbol $\varphi(s)=\sigma+\sum_{j=1}^{d}r_jp_j^{-s}$ satisfying $\sigma>1/2$ and $\sum_{j=1}^{d}r_j\leq\sigma-1/2$.

Background

The paper studies finite-prime symbols on the Hardy space $\mathcal H^2$ of Dirichlet series and obtains sharp asymptotic information in the critical regime, a second-order expansion for fixed $\sigma$, and explicit finite-dimensional approximation bounds. It also identifies the limiting operator and characterizes its equality cases under the concentration inequality.

Despite these results, the authors explicitly state that they do not obtain an exact closed expression for the norm of a general finite-prime symbol. Thus the general exact norm problem remains unresolved beyond the special one-prime and asymptotic settings treated in the paper.