# Moscow Mathematical Journal

Volume 22, Issue 4, October–December 2022  pp. 741–757.

On the $a$-Points of Symmetric Sum of Multiple Zeta Function

Authors:  Hideki Murahara (1) and Tomokazu Onozuka (2)
Author institution:(1) Nakamura Gakuen University Graduate School, 5-7-1, Befu, Jonan-ku, Fukuoka, 814-0198, Japan
(2) Multiple Zeta Research Center, Kyushu University 744, Motooka, Nishi-ku, Fukuoka, 819-0395, Japan

Summary:

In this paper, we present some results on the $a$-points of the symmetric sum of the Euler–Zagier multiple zeta function. Our first three results are for the $a$-points free region of the function. The fourth result is the Riemann–von Mangoldt type formula. In the last two results, we study the real parts of $a$-points of the function.

2020 Math. Subj. Class. Primary: 11M32.

Keywords: Multiple zeta function, the Riemann zeta function, the Riemann–von Mangoldt formula, $a$-point.