On restricted sum formulas for multiple zeta values with even arguments

The main goal of this paper is the presentation of an elementary analytic technique which enables the evaluation of the so-called restricted sum formulas involving multiple zeta values with even arguments, i.e. E(2c,K):=∑∑j=1Kcj=ccj∈Nζ(2c1,…,2cK),\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$E(2c,K):=\sum_{\substack{\sum_{j=1}^{K}c_{j}=c\\{c}_{j}\in\mathbb{N}}} \zeta(2c_1,\ldots ,2c_K),$$\end{document}where c and K are arbitrary positive integers with c≥K\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${c\ge K}$$\end{document}. Though the young and general theory of the multiple Riemann zeta function with a rich application potential may be rather complicated, our contribution makes the evaluation of the term E(2c,K) intelligible to a broad mathematical audience.