A question about convergence of functions involving Q-Pochhammer symbols

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Consider the function $H:\mathbb{C}\rightarrow\mathbb{C}$:

$$H(s)=\prod_{n=1}^{\infty}\left(1+\frac{1}{2^{ns}}\right)$$

$H(s)$ is convergent on $\Re(s)>0$. Is it absolutely convergent on $\Re(s)>1$