Sums of Products of Riemann Zeta Tails

TL;DR

This paper extends results on sums of products of Riemann zeta tails by using multiple zeta values, weakening hypotheses and generalizing to products of three or more tails.

Contribution

It introduces a new approach using multiple zeta values to prove and generalize results on Riemann zeta tails under weaker assumptions.

Findings

Results can be proved with weaker hypotheses

Generalization to products of three or more tails

Connections to multiple zeta values

Abstract

A recent paper of Furdui and Valean proves some results about sums of products of "tails" of the series for the Riemann zeta function. We show how such results can be proved with weaker hypotheses using multiple zeta values, and also show how they can be generalized to products of three or more such tails.