  In this paper we study the problem of counting Salem numbers of fixed degree.
Given a set of disjoint intervals $I_1,\ldots, I_{k}\subset
\left[0;\pi\right]$, $1\leq k\leq m$ let $Sal_{m,k}(Q,I_1,\ldots,I_{k})$ denote
the set of ordered $(k+1)$-tuples $\left(\alpha_0,\ldots,\alpha_{k}\right)$ of
conjugate algebraic integers, such that $\alpha_0$ is a Salem numbers of degree
$2m+2$ satisfying $\alpha\leq Q$ for some positive real number $Q$ and
$\arg\alpha_i\in I_i$. We derive the following asymptotic approximation
  \[
  \#
Sal_{m,k}(Q,I_1,\ldots,I_{k})=\omega_m\,Q^{m+1}\,\int\limits_{I_1}\ldots\int\limits_{I_{k}}\rho_{m,k}(\boldsymbol\theta)\rm
d\boldsymbol\theta+O\left(Q^{m}\right),\quad Q\rightarrow\infty,
  \]
  providing explicit expressions for the constant $\omega_m$ and the function
$\rho_{m,k}(\boldsymbol\theta)$.
  Moreover we derive a similar asymptotic formula for the set of all Salem
numbers of fixed degree and absolute value bounded by $Q$ as
$Q\rightarrow\infty$.
