The convergence of series of simple fractions in $L_p(\mathbb R)$.

The convergence of series of simple fractions in $L_p(\mathbb R)$ has been investigated. In particular, necessary and sufficient conditions for the convergence of series with coefficients $\frac{p_k}{t-z_k}$, where $p_k$ is a sequence of positive numbers, in $L_p(\mathbb R)$ have been obtained.