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Zeta functions are typically analogues or generalizations of the Riemann zeta function. Examples include Dedekind zeta functions of number fields, and zeta functions of varieties over finite fields. They are typically initially defined as formal generating functions, but often admit analytic continuations.
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What does this connection between Chebyshev, Ramanujan, Ihara and Riemann mean?
It all started with Chris' answer saying returning paths on cubic graphs without backtracking can be expressed by the following recursion relation:
$$p_{r+1}(a) = ap_r(a)-2p_{r-1}(a)$$
$a$ is an …
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How does the topology of the graphs' Riemann surface relate to its knot representation?
Let's consider the following bipartite cubic planar non-simple graph
$\hskip2.3in$
Looking at the orientation of the edges around the vertices, it is obvious that left and right are oriented opposite. …