SPANNING TREES IN
$\mathbb {Z}$
-COVERS OF A FINITE GRAPH AND MAHLER MEASURES
RICCARDO PENGO,
DANIEL VALLIÈRES
Abstract:Using the special value at
$u=1$
of Artin–Ihara L-functions, we associate to every
$\mathbb {Z}$
-cover of a finite connected graph a polynomial, which we call the Ihara polynomial. We show that the number of spanning trees for the finite intermediate graphs of such a cover can be expressed in terms of the Pierce–Lehmer sequence associated to a factor of the Ihara polynomial. This allows us to express the asymptotic growth of the number of spanning tre… Show more
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