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In this paper we investigate the distribution of zeros of the independencepolynomial of hypergraphs of maximum degree $\Delta$. For graphs the largestzero-free disk around zero was described by Shearer as having radius$\lambda_s(\Delta)=(\Delta-1)^{\Delta-1}/\Delta^\Delta$. Recently it was shownby Galvin et al. that for hypergraphs the disk of radius $\lambda_s(\Delta+1)$is zero-free; however, it was conjectured that the actual truth should be$\lambda_s(\Delta)$. We show that this is indeed the case. We also show thatthere exists an open region around the interval$[0,(\Delta-1)^{\Delta-1}/(\Delta-2)^\Delta)$ that is zero-free for hypergraphsof maximum degree $\Delta$, which extends the result of Peters and Regts fromgraphs to hypergraphs. Finally, we determine the radius of the largestzero-free disk for the family of bounded degree $k$-uniform linear hypertreesin terms of $k$ and $\Delta$.

Optimal zero-free regions for the independence polynomial of bounded degree hypergraphs