A note on infinite divisibility of zeta distributions (Q2908315)

It is well known that the normalized zeta distribution is infinitely divisible; see [\textit{B. V. Gnedenko} and \textit{A. N. Kolmogorov}, Limit distributions for sums of independent random variables. Cambridge: Addison-Wesley Publishing Company (1954; Zbl 0056.36001)]. The authors give two proofs of this result. Then, they consider the multiple zeta-star function NEWLINE\[NEWLINE \zeta^*(s_1,\dotsc ,s_d)=\sum\limits_{m_1\geq \dotsb \geq m_d\geq 1}\frac{1}{m_1^{s_1}\dotsm m_d^{s_d}} NEWLINE\]NEWLINE and show that the corresponding distribution is not infinitely divisible.