Monotonicity of Coefficients of Interpolated Multiple Zeta Values

Let ${\zeta }^t(\mathit{k})={\sum }_{d=1}^r{S}_d(\mathit{k})t^{r-d}$ be the interpolated multiple zeta value of an admissible index $\mathit{k}$ of depth $r$. We show the monotonicity property of coefficients $S_1(\mathit{k})\ge \cdots \ge S_r(\mathit{k})>0$. In the proof, we represent the coefficients as integrals over a common measure space and compares the integrands pointwise. As consequences, we determine the sign and vanishing of ${\zeta }^{-1}(\mathit{k})$ and locate the zeros of ${\zeta }^t(\mathit{k})$ in the closed unit disk.