  We consider the space $\mathcal{H}(ces_p)$ of all Dirichlet series whose
coefficients belong to the Ces\`{a}ro sequence space $ces_p$, consisting of all
complex sequences whose absolute Ces\`{a}ro means are in $\ell^p$, for
$1<p<\infty$. It is a Banach space of analytic functions, for which we study
the maximal domain of analyticity and the boundedness of point evaluations. We
identify the algebra of analytic multipliers on $\mathcal{H}(ces_p)$ as the
Wiener algebra of Dirichlet series shifted to the vertical half-plane
$\mathbb{C}_{1/q}:=\{s\in\mathbb{C}:\Re s>1/q\}$, where $1/p+1/q=1$.
