Value-distribution of Euler--Zagier type multiple zeta-functions with identical arguments on the critical line

Source abstract

We consider the value-distribution of the Euler--Zagier type multiple zeta-functions with identical arguments on the critical line. Mishou showed that the set of the values of the Euler--Zagier double sum with identical arguments on the critical line is dense in the complex plane under the Riemann Hypothesis. In this paper, we generalize Mishou's result to the $r$-fold Euler--Zagier multiple zeta-functions with identical arguments for $r geq 4$.