Riesz mean

Summary

A Riesz mean of a series $\sum a_n$ is a weighted partial sum in which the term $a_n$ is damped by a factor $(1 - \lambda_n/\omega)^{\delta}$. Here $\lambda_n$ is a given increasing sequence and $\omega$ is a cut-off that grows to infinity. The series is Riesz summable when these means converge. With $\lambda_n = n$ and $\delta = 1$ the Riesz means at integer cut-offs are the Cesàro means of the partial sums. Riesz means with $\lambda_n = \ln n$ are a standard tool for Dirichlet series in analytic number theory.