Zeta Functions of Weighted Graphs and Covering Graphs
نویسندگان
چکیده
We nd a condition for weights on the edges of a graph which insures that the Ihara zeta function has a 3-term determinant formula. Then we investigate the locations of poles of abelian graph coverings and compare the results with random covers. We discover that the zeta function of the random cover satis es an approximate Riemann hypothesis while that of the abelian cover does not.
منابع مشابه
Weighted Zeta Functions of Graph Coverings
We present a decomposition formula for the weighted zeta function of an irregular covering of a graph by its weighted L-functions. Moreover, we give a factorization of the weighted zeta function of an (irregular or regular) covering of a graph by equivalence classes of prime, reduced cycles of the base graph. As an application, we discuss the structure of balanced coverings of signed graphs.
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