The paper “Cesaro summation by spheres of lattice sums and Madelung constants” co-authored by Benjamin Galbally and Sergey Zelik, has been accepted for publication in Communications in Pure and Applied Analysis (link here). The final form arXiv version is available here. The paper studies convergence of 3D lattice sums via expanding spheres, proving that these series remain convergent in Cesaro sense. For the case of second order Cesaro summation, we present an elementary proof of convergence. The proof for first order Cesaro summation is more involved and is based on Riemann localization for multi-dimensional Fourier series.