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IHARA’S ZETA FUNCTION FOR PERIODIC GRAPHS AND ITS APPROXIMATION IN THE AMENABLE CASE
, 2008
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Ihara zeta functions for periodic SIMPLE GRAPHS
, 2008
"... The definition and main properties of the Ihara zeta function for graphs are reviewed, focusing mainly on the case of periodic simple graphs. Moreover, we give a new proof of the associated determinant formula, based on the treatment developed by Stark and Terras for finite graphs. ..."
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Cited by 11 (4 self)
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The definition and main properties of the Ihara zeta function for graphs are reviewed, focusing mainly on the case of periodic simple graphs. Moreover, we give a new proof of the associated determinant formula, based on the treatment developed by Stark and Terras for finite graphs.
A C∗algebra of geometric operators on selfsimilar CWcomplexes. Novikov–Shubin and L²Betti numbers
, 2006
"... A class of CWcomplexes, called selfsimilar complexes, is introduced, together with C∗algebras Aj of operators, endowed with a finite trace, acting on squaresummable cellular jchains. Since the Laplacian ∆j belongs to Aj, L²Betti numbers and NovikovShubin numbers are defined for such complexes ..."
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Cited by 2 (2 self)
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A class of CWcomplexes, called selfsimilar complexes, is introduced, together with C∗algebras Aj of operators, endowed with a finite trace, acting on squaresummable cellular jchains. Since the Laplacian ∆j belongs to Aj, L²Betti numbers and NovikovShubin numbers are defined for such complexes in terms of the trace. In particular a relation involving the EulerPoincaré characteristic is proved. L²Betti and NovikovShubin numbers are computed for some selfsimilar complexes arising from selfsimilar fractals.
Bartholdi zeta functions for periodic simple graphs
, 2008
"... The definition of the Bartholdi zeta function is extended to the case of infinite periodic graphs. By means of the analytic determinant for semifinite von Neumann algebras studied by the authors in [7], a determinant formula and functional equations are obtained for this zeta function. ..."
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Cited by 2 (1 self)
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The definition of the Bartholdi zeta function is extended to the case of infinite periodic graphs. By means of the analytic determinant for semifinite von Neumann algebras studied by the authors in [7], a determinant formula and functional equations are obtained for this zeta function.
Bartholdi Zeta Functions of Fractal Graphs
"... Recently, Guido, Isola and Lapidus [11] defined the Ihara zeta function of a fractal graph, and gave a determinant expression of it. We define the Bartholdi zeta function of a fractal graph, and present its determinant expression. 1 ..."
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Recently, Guido, Isola and Lapidus [11] defined the Ihara zeta function of a fractal graph, and gave a determinant expression of it. We define the Bartholdi zeta function of a fractal graph, and present its determinant expression. 1
ZETA FUNCTIONS OF INFINITE GRAPH BUNDLES
, 2007
"... Abstract. We compute the equivariant zeta function for bundles over infinite graphs and for infinite covers. In particular, we give a “transfer formula ” for the zeta function of infinite graph covers. Also, when the infinite cover is given as a limit of finite covers, we give a formula for the limi ..."
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Abstract. We compute the equivariant zeta function for bundles over infinite graphs and for infinite covers. In particular, we give a “transfer formula ” for the zeta function of infinite graph covers. Also, when the infinite cover is given as a limit of finite covers, we give a formula for the limit of the zeta functions. 1.