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{\bf Christopher K. Storm}
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{\bf The Zeta Function of a Hypergraph}
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We generalize the Ihara-Selberg zeta function to hypergraphs in a
natural way. Hashimoto's factorization results for biregular
bipartite graphs apply, leading to exact factorizations. For
$(d,r)$-regular hypergraphs, we show that a modified Riemann
hypothesis is true if and only if the hypergraph is Ramanujan in the
sense of Winnie Li and Patrick Sol\'e. Finally, we give an example to
show how the generalized zeta function can be applied to graphs to
distinguish non-isomorphic graphs with the same Ihara-Selberg zeta
function.
\bye