No Access

THE IHARA-SELBERG ZETA FUNCTION OF A TREE LATTICE

HYMAN BASS

HYMAN BASS

Department of Mathematics, Columbia University, New York, NY 10027, USA

Search for more papers by this author

https://doi.org/10.1142/S0129167X92000357Cited by:163

Partially supported by NSF Grant DMS 8802181

AMSC: 05C05, 05C25, 05C50, 11F72, 15A15, 16A27

- Cited By 163
  - Non-backtracking cycles: length spectrum theory and graph mining applications
    Leo Torres, Pablo Suárez-Serrato and Tina Eliassi-Rad
    25 June 2019 | Applied Network Science, Vol. 4, No. 1
  - The partial differential coefficients for the second weighted Bartholdi zeta function of a graph
    Shigeki Matsutani, Hideo Mitsuhashi, Hideaki Morita and Iwao Sato
    1 Sep 2019 | Discrete Mathematics, Vol. 342, No. 9
  - Ihara Zeta Function and Spectrum of the Cone Over a Semiregular Bipartite Graph
    Deqiong Li and Yaoping Hou
    13 August 2019 | Graphs and Combinatorics, Vol. 29
  - Building lattices and zeta functions
    Anton Deitmar, Ming-Hsuan Kang and Rupert McCallum
    4 Jul 2019 | Advances in Geometry, Vol. 0, No. 0
  - Local Kesten–McKay Law for Random Regular Graphs
    Roland Bauerschmidt, Jiaoyang Huang and Horng-Tzer Yau
    28 February 2019 | Communications in Mathematical Physics, Vol. 369, No. 2
  - Eigenvalue monotonicity of q-Laplacians of trees along a poset
    Mukesh Kumar Nagar
    1 Jun 2019 | Linear Algebra and its Applications, Vol. 571
  - A new weighted Ihara zeta function for a graph
    Norio Konno, Hideo Mitsuhashi, Hideaki Morita and Iwao Sato
    1 Jun 2019 | Linear Algebra and its Applications, Vol. 571
  - A new generalized Bartholdi zeta function for a digraph
    Hideo Mitsuhashi, Hideaki Morita and Iwao Sato
    24 May 2019 | Linear and Multilinear Algebra, Vol. 7
  - Graph comparison via the nonbacktracking spectrum
    Andrew Mellor and Angelica Grusovin
    23 May 2019 | Physical Review E, Vol. 99, No. 5
  - Laplacian immanantal polynomials and the GTS poset on trees
    Mukesh Kumar Nagar and Sivaramakrishnan Sivasubramanian
    1 Jan 2019 | Linear Algebra and its Applications, Vol. 561
  - Non-Backtracking Centrality Based Random Walk on Networks
    Yuan Lin, Zhongzhi Zhang and Prudence Wong
    24 March 2018 | The Computer Journal, Vol. 62, No. 1
  - Zeta and L-functions of finite quotients of apartments and buildings
    Ming-Hsuan Kang, Wen-Ching Winnie Li and Chian-Jen Wang
    1 August 2018 | Israel Journal of Mathematics, Vol. 228, No. 1
  - Fundamentals of spreading processes in single and multilayer complex networks
    Guilherme Ferraz de Arruda, Francisco A. Rodrigues and Yamir Moreno
    1 Oct 2018 | Physics Reports, Vol. 756
  - Zeta functions from graphs
    Simon Davis
    1 Aug 2018 | AKCE International Journal of Graphs and Combinatorics, Vol. 15, No. 2
  - The Arithmetic Tutte polynomial of two matrices associated to Trees
    R. B. Bapat and Sivaramakrishnan Sivasubramanian
    1 Aug 2018 | Special Matrices, Vol. 6, No. 1
  - Limiting eigenvalue distribution of random matrices of Ihara zeta function of long-range percolation graphs
    O. Khorunzhiy
    19 June 2018 | Random Matrices: Theory and Applications, Vol. 07, No. 03
  - The weighted Kirchhoff index of a graph
    Hideo Mitsuhashi, Hideaki Morita and Iwao Sato
    1 Jun 2018 | Linear Algebra and its Applications, Vol. 547
  - A note on Bartholdi zeta function and graph invariants based on resistance distance
    Deqiong Li and Yaoping Hou
    1 Mar 2018 | Discrete Mathematics, Vol. 341, No. 3
  - Bartholdi Zeta Functions of Generalized Join Graphs
    Haiyan Chen and Yu Chen
    27 December 2017 | Graphs and Combinatorics, Vol. 34, No. 1
  - Improved collective influence of finding most influential nodes based on disjoint-set reinsertion
    Fengkuangtian Zhu
    2018 | Scientific Reports, Vol. 8, No. 1
  - Quaternionic Grover Walks and Zeta Functions of Graphs with Loops
    Norio Konno, Hideo Mitsuhashi and Iwao Sato
    25 May 2017 | Graphs and Combinatorics, Vol. 33, No. 6
  - Closed geodesics and bounded gaps
    Anton Deitmar
    26 December 2016 | Mathematische Zeitschrift, Vol. 287, No. 1-2
  - Quantum Ergodicity on Regular Graphs
    Nalini Anantharaman
    5 May 2017 | Communications in Mathematical Physics, Vol. 353, No. 2
  - Graph Characterization by Counting Sink Star Subgraphs
    Maedeh S. Tahaei and Seyed Naser Hashemi
    8 October 2016 | Journal of Mathematical Imaging and Vision, Vol. 57, No. 3
  - On a construction using commuting regular graphs
    Marius Somodi, Katie Burke and Jesse Todd
    1 Mar 2017 | Discrete Mathematics, Vol. 340, No. 3
  - On the Ihara zeta function and resistance distance-based indices
    Marius Somodi
    1 Jan 2017 | Linear Algebra and its Applications, Vol. 513
  - How well do local algorithms solve semidefinite programs?
    Zhou Fan and Andrea Montanari
    1 Jan 2017
  - The Discrete-time Quaternionic Quantum Walk and the Second Weighted Zeta Function on a Graph
    Norio KONNO, Hideo MITSUHASHI and Iwao SATO
    1 Jan 2017 | Interdisciplinary Information Sciences, Vol. 23, No. 1
  - The quaternionic second weighted zeta function of a graph and the Study determinant
    Norio Konno, Hideo Mitsuhashi and Iwao Sato
    1 Dec 2016 | Linear Algebra and its Applications, Vol. 510
  - The quaternionic weighted zeta function of a graph
    Norio Konno, Hideo Mitsuhashi and Iwao Sato
    2 May 2016 | Journal of Algebraic Combinatorics, Vol. 44, No. 3
  - The coefficients of the reduced Bartholdi zeta function
    Maedeh S. Tahaei and Seyed Naser Hashemi
    1 Nov 2016 | Linear Algebra and its Applications, Vol. 509
  - Statistical physics of inference: thresholds and algorithms
    Lenka Zdeborová and Florent Krzakala
    19 August 2016 | Advances in Physics, Vol. 65, No. 5
  - On graph theory Mertens’ theorems
    Takehiro Hasegawa and Seiken Saito
    12 May 2016 | Graphs and Combinatorics, Vol. 32, No. 5
  - Cutoff on all Ramanujan graphs
    Eyal Lubetzky and Yuval Peres
    30 September 2016 | Geometric and Functional Analysis, Vol. 26, No. 4
  - A New Proof of a Formula for the Bartholdi Zeta Function of a Digraph
    Iwao Sato
    23 December 2015 | Graphs and Combinatorics, Vol. 32, No. 4
  - Depth-based hypergraph complexity traces from directed line graphs
    Lu Bai, Francisco Escolano and Edwin R. Hancock
    1 Jun 2016 | Pattern Recognition, Vol. 54
  - Leveraging percolation theory to single out influential spreaders in networks
    Filippo Radicchi and Claudio Castellano
    22 June 2016 | Physical Review E, Vol. 93, No. 6
  - A generalized Bartholdi zeta function for a general graph
    Iwao Sato, Hideo Mitsuhashi and Hideaki Morita
    3 August 2015 | Linear and Multilinear Algebra, Vol. 64, No. 5
  - Beyond the locally treelike approximation for percolation on real networks
    Filippo Radicchi and Claudio Castellano
    23 March 2016 | Physical Review E, Vol. 93, No. 3
  - The discrete-time quaternionic quantum walk on a graph
    Norio Konno, Hideo Mitsuhashi and Iwao Sato
    12 December 2015 | Quantum Information Processing, Vol. 15, No. 2
  - Graph Entropy from Closed Walk and Cycle Functionals
    Furqan Aziz, Edwin R. Hancock and Richard C. Wilson
    5 November 2016
  - Non-Backtracking Random Walks and a Weighted Ihara’s Theorem
    Mark Kempton
    1 Jan 2016 | Open Journal of Discrete Mathematics, Vol. 06, No. 04
  - A Balanced Signed Digraph
    Yusuke Higuchi and Iwao Sato
    8 November 2014 | Graphs and Combinatorics, Vol. 31, No. 6
  - Heat kernels on regular graphs and generalized Ihara zeta function formulas
    G. Chinta, J. Jorgenson and A. Karlsson
    23 September 2014 | Monatshefte für Mathematik, Vol. 178, No. 2
  - Distinguishing graphs with zeta functions and generalized spectra
    Christina Durfee and Kimball Martin
    1 Sep 2015 | Linear Algebra and its Applications, Vol. 481
  - Seiberg duality, quiver gauge theories, and Ihara’s zeta function
    Da Zhou
    ,
    Yan Xiao
    and
    Yang-Hui He
    8 July 2015 | International Journal of Modern Physics A, Vol. 30, No. 18n19
  - Spectral detection in the censored block model
    Alaa Saade, Marc Lelarge, Florent Krzakala and Lenka Zdeborova
    1 Jun 2015
  - Artin L -Functions on Finite Quotients of PGL 3
    Ming-Hsuan Kang and Wen-Ching Winnie Li
    1 December 2014 | International Mathematics Research Notices, Vol. 2015, No. 19
  - Ihara Zeta Functions of Infinite Weighted Graphs
    Anton Deitmar
    1 Jan 2015 | SIAM Journal on Discrete Mathematics, Vol. 29, No. 4
  - On a prime zeta function of a graph
    Takehiro Hasegawa and Seiken Saito
    1 January 2015 | Pacific Journal of Mathematics, Vol. 273, No. 1
  - A remark on zeta functions of finite graphs via quantum walks
    Yusuke Higuchi, Norio Konno, Iwao Sato and Etsuo Segawa
    11 September 2014 | Pacific Journal of Mathematics for Industry, Vol. 6, No. 1
  - Zeta functions and complexities of middle graphs of semiregular bipartite graphs
    Iwao Sato
    1 Nov 2014 | Discrete Mathematics, Vol. 335
  - Periodic Walks on Large Regular Graphs and Random Matrix Theory
    Idan Oren and Uzy Smilansky
    14 November 2014 | Experimental Mathematics, Vol. 23, No. 4
  - Ihara zeta functions and cospectrality of joins of regular graphs
    Andrea Blanchard, Ehrich Pakala and Marius Somodi
    1 Oct 2014 | Discrete Mathematics, Vol. 333
  - Spectral density of the non-backtracking operator on random graphs
    A. Saade, F. Krzakala and L. Zdeborová
    3 September 2014 | EPL (Europhysics Letters), Vol. 107, No. 5
  - Directed Depth-Based Complexity Traces of Hypergraphs from Directed Line Graphs
    Lu Bai, Edwin R. Hancock, Peng Ren and Francisco Escolano
    1 Aug 2014
  - Zeta functions of complexes arising from PGL(3)
    Ming-Hsuan Kang and Wen-Ching Winnie Li
    1 May 2014 | Advances in Mathematics, Vol. 256
  - New proofs of Bapat and Sivasubramanian's theorems
    Iwao Sato
    1 May 2014 | Linear Algebra and its Applications, Vol. 448
  - Some weighted Bartholdi zeta function of a digraph
    Hirobumi Mizuno and Iwao Sato
    1 Mar 2014 | Linear Algebra and its Applications, Vol. 445
  - A matrix-weighted zeta function of a graph
    Iwao Sato, Hideo Mitsuhashi and Hideaki Morita
    13 February 2013 | Linear and Multilinear Algebra, Vol. 62, No. 1
  - Cycle Statistics in Complex Networks and Ihara’s Zeta Function
    Clara Grácio, Anthony C. C. Coolen and Alessia Annibale
    15 January 2014
  - Spectral redemption in clustering sparse networks
    F. Krzakala, C. Moore, E. Mossel, J. Neeman and A. Sly et al.
    25 November 2013 | Proceedings of the National Academy of Sciences, Vol. 110, No. 52
  - On the Ihara Zeta Function of Cones Over Regular Graphs
    Paymun Bayati and Marius Somodi
    17 October 2012 | Graphs and Combinatorics, Vol. 29, No. 6
  - Graph reconstruction and quantum statistical mechanics
    Gunther Cornelissen and Matilde Marcolli
    1 Oct 2013 | Journal of Geometry and Physics, Vol. 72
  - K -theory of locally finite graph C∗ -algebras
    Natalia Iyudu
    1 Sep 2013 | Journal of Geometry and Physics, Vol. 71
  - Backtrackless Walks on a Graph
    F. Aziz, R. C. Wilson and E. R. Hancock
    1 Jun 2013 | IEEE Transactions on Neural Networks and Learning Systems, Vol. 24, No. 6
  - A generalized Bartholdi zeta function for a regular covering of a bipartite graph
    Iwao Sato and Seiken Saito
    1 Feb 2013 | Linear Algebra and its Applications, Vol. 438, No. 3
  - Geometricity and Embedding
    Peng Ren, Furqan Aziz, Lin Han, Eliza Xu and Richard C. Wilson et al.
    1 Jan 2013
  - Discrete Graphs – A Paradigm Model for Quantum Chaos
    Uzy Smilansky
    18 October 2013
  - Introduction
    Toshikazu Sunada
    5 October 2012
  - Discrete Abel–Jacobi Maps
    Toshikazu Sunada
    5 October 2012
  - Quotient Objects
    Toshikazu Sunada
    5 October 2012
  - Generalities on Graphs
    Toshikazu Sunada
    5 October 2012
  - Homology Groups of Graphs
    Toshikazu Sunada
    5 October 2012
  - Covering Graphs
    Toshikazu Sunada
    5 October 2012
  - Topological Crystals
    Toshikazu Sunada
    5 October 2012
  - Standard Realizations
    Toshikazu Sunada
    5 October 2012
  - Explicit Construction
    Toshikazu Sunada
    5 October 2012
  - Random Walks on Topological Crystals
    Toshikazu Sunada
    5 October 2012
  - The Third Immanant of q-Laplacian Matrices of Trees and Laplacians of Regular Graphs
    R. B. Bapat and Sivaramakrishnan Sivasubramanian
    1 Jan 2013
  - Enumeration of graphs with the same Ihara zeta function
    A. Setyadi and C.K. Storm
    1 Jan 2013 | Linear Algebra and its Applications, Vol. 438, No. 1
  - Nodal count of graph eigenfunctions via magnetic perturbation
    Gregory Berkolaiko
    3 November 2013 | Analysis & PDE, Vol. 6, No. 5
  - The Critical Ising Model via Kac-Ward Matrices
    David Cimasoni
    5 October 2012 | Communications in Mathematical Physics, Vol. 316, No. 1
  - Edge zeta functions of hypergraphs
    Iwao Sato
    29 February 2012 | Journal of Applied Mathematics and Computing, Vol. 40, No. 1-2
  - Bass’ identity and a coin arrangements lemma
    Hossein Teimoori Faal and Martin Loebl
    1 Jul 2012 | European Journal of Combinatorics, Vol. 33, No. 5
  - On the relation between quantum walks and zeta functions
    Norio Konno and Iwao Sato
    24 May 2011 | Quantum Information Processing, Vol. 11, No. 2
  - The edge L-function of a graph
    Iwao Sato and Seiken Saito
    1 Mar 2012 | Linear Algebra and its Applications, Vol. 436, No. 5
  - Efficient computation of Ihara coefficients using the Bell polynomial recursion
    Samuel Rota Bulò, Edwin R. Hancock, Furqan Aziz and Marcello Pelillo
    1 Mar 2012 | Linear Algebra and its Applications, Vol. 436, No. 5
  - New proofs for Levine’s theorems
    Iwao Sato
    1 Sep 2011 | Linear Algebra and its Applications, Vol. 435, No. 5
  - Identities for minors of the Laplacian, resistance and distance matrices
    R.B. Bapat and Sivaramakrishnan Sivasubramanian
    1 Sep 2011 | Linear Algebra and its Applications, Vol. 435, No. 6
  - A polynomial characterization of hypergraphs using the Ihara zeta function
    Peng Ren, Tatjana Aleksić, Richard C. Wilson and Edwin R. Hancock
    1 Sep 2011 | Pattern Recognition, Vol. 44, No. 9
  - Zeta functions of quantum graphs
    J M Harrison and K Kirsten
    11 May 2011 | Journal of Physics A: Mathematical and Theoretical, Vol. 44, No. 23
  - Quantum walks, Ihara zeta functions and cospectrality in regular graphs
    Peng Ren, Tatjana Aleksić, David Emms, Richard C. Wilson and Edwin R. Hancock
    27 October 2010 | Quantum Information Processing, Vol. 10, No. 3
  - Some properties of graphs determined by edge zeta functions
    Christopher Storm
    1 Mar 2011 | Linear Algebra and its Applications, Vol. 434, No. 5
  - Graph Characterization via Ihara Coefficients
    Peng Ren, R C Wilson and E R Hancock
    1 Feb 2011 | IEEE Transactions on Neural Networks, Vol. 22, No. 2
  - Kernelising the Ihara Zeta Function
    Furqan Aziz, Richard C. Wilson and Edwin R. Hancock
    1 Jan 2011
  - Graph Characterization via Backtrackless Paths
    Furqan Aziz, Richard C. Wilson and Edwin R. Hancock
    1 Jan 2011
  - Bartholdi zeta functions of periodic graphs
    Iwao Sato
    1 Jan 2011 | Linear and Multilinear Algebra, Vol. 59, No. 1
  - Weighted zeta functions for quotients of regular coverings of graphs
    Seiya Negami and Iwao Sato
    1 Nov 2010 | Advances in Mathematics, Vol. 225, No. 4
  - ζ-regularized spectral determinants on metric graphs
    Christophe Texier
    30 September 2010 | Journal of Physics A: Mathematical and Theoretical, Vol. 43, No. 42
  - Weighted scattering matrices of regular coverings of graphs
    Hirobumi Mizuno and Iwao Sato
    1 Oct 2010 | Linear and Multilinear Algebra, Vol. 58, No. 7
  - A generalized Kac–Ward formula
    David Cimasoni
    30 July 2010 | Journal of Statistical Mechanics: Theory and Experiment, Vol. 2010, No. 07
  - Belief propagation and loop calculus for the permanent of a non-negative matrix
    Yusuke Watanabe and Michael Chertkov
    25 May 2010 | Journal of Physics A: Mathematical and Theoretical, Vol. 43, No. 24
  - “Almost divisibility” in the Ihara zeta functions of certain ramified covers of q+1-regular graphs
    Beth Malmskog and Michelle Manes
    1 May 2010 | Linear Algebra and its Applications, Vol. 432, No. 10
  - Scattering matrices of regular coverings of graphs
    Hirobumi Mizuno and Iwao Sato
    1 Feb 2010 | Discrete Mathematics, Vol. 310, No. 4
  - Zeta functions of infinite graph bundles
    Samuel Cooper and Stratos Prassidis
    1 Feb 2010 | Linear and Multilinear Algebra, Vol. 58, No. 2
  - Ihara Coefficients: A Flexible Tool for Higher Order Learning
    Peng Ren, Tatjana Aleksić, Richard C. Wilson and Edwin R. Hancock
    1 Jan 2010
  - Trace formulae and spectral statistics for discrete Laplacians on regular graphs ( I )
    Idan Oren, Amit Godel and Uzy Smilansky
    29 September 2009 | Journal of Physics A: Mathematical and Theoretical, Vol. 42, No. 41
  - Weighted graph characteristics from oriented line graph polynomials
    Peng Ren, Richard C Wilson and Edwin R Hancock
    1 Sep 2009
  - The enumeration of planar graphs via Wick's theorem
    Mihyun Kang and Martin Loebl
    1 Aug 2009 | Advances in Mathematics, Vol. 221, No. 5
  - An Ihara formula for partially directed graphs
    Andrei Tarfulea and Robert Perlis
    1 Jul 2009 | Linear Algebra and its Applications, Vol. 431, No. 1-2
  - A new Bartholdi zeta function of a digraph II
    Hirobumi Mizuno and Iwao Sato
    1 May 2009 | Discrete Mathematics, Vol. 309, No. 10
  - Optimal Bipartite Ramanujan Graphs from Balanced Incomplete Block Designs: Their Characterizations and Applications to Expander/LDPC Codes
    Tom Høholdt and Heeralal Janwal
    1 Jan 2009
  - Zeta functions of graphs with Z actions
    Bryan Clair
    1 Jan 2009 | Journal of Combinatorial Theory, Series B, Vol. 99, No. 1
  - Pattern vectors from the Ihara zeta function
    Peng Ren, Richard C. Wilson and Edwin R. Hancock
    1 Dec 2008
  - The stochastic weighted complexity of a group covering of a digraph
    Iwao Sato
    1 Oct 2008 | Linear Algebra and its Applications, Vol. 429, No. 8-9
  - Ihara's zeta function for periodic graphs and its approximation in the amenable case
    Daniele Guido, Tommaso Isola and Michel L. Lapidus
    1 Sep 2008 | Journal of Functional Analysis, Vol. 255, No. 6
  - Generalized characteristic polynomials of graph bundles
    Dongseok Kim, Hye Kyung Kim and Jaeun Lee
    1 Aug 2008 | Linear Algebra and its Applications, Vol. 429, No. 4
  - Weighted Bartholdi zeta functions of graph coverings
    Iwao Sato
    1 Jun 2008 | Discrete Mathematics, Vol. 308, No. 12
  - On the K-Theory of Graph C *-Algebras
    Gunther Cornelissen, Oliver Lorscheid and Matilde Marcolli
    25 January 2008 | Acta Applicandae Mathematicae, Vol. 102, No. 1
  - Bartholdi Zeta Functions of Branched Coverings of Digraphs
    Hirobumi Mizuno and Iwao Sato
    1 Jan 2008
  - Graph Characteristics from the Ihara Zeta Function
    Peng Ren, Richard C. Wilson and Edwin R. Hancock
    1 Jan 2008
  - The coefficients of the Ihara zeta function
    Geoffrey Scott and Christopher Storm
    1 July 2008 | Involve, a Journal of Mathematics, Vol. 1, No. 2
  - Quantum graphs where back-scattering is prohibited
    J M Harrison, U Smilansky and B Winn
    6 November 2007 | Journal of Physics A: Mathematical and Theoretical, Vol. 40, No. 47
  - Bartholdi zeta and L-functions of weighted digraphs, their coverings and products
    Young-Bin Choe, Jin Ho Kwak, Yong Sung Park and Iwao Sato
    1 Aug 2007 | Advances in Mathematics, Vol. 213, No. 2
  - Ihara zeta functions of digraphs
    Matthew D. Horton
    1 Aug 2007 | Linear Algebra and its Applications, Vol. 425, No. 1
  - A new Bartholdi zeta function of a digraph
    Hirobumi Mizuno and Iwao Sato
    1 Jun 2007 | Linear Algebra and its Applications, Vol. 423, No. 2-3
  - Zeta functions and complexities of a semiregular bipartite graph and its line graph
    Iwao Sato
    1 Jan 2007 | Discrete Mathematics, Vol. 307, No. 2
  - ZETA FUNCTIONS OF GRAPH BUNDLES
    Rongquan Feng and Jin-Ho Kwak
    1 Nov 2006 | Journal of the Korean Mathematical Society, Vol. 43, No. 6
  - A non-commutative formula for the colored Jones function
    Stavros Garoufalidis and Martin Loebl
    2 August 2006 | Mathematische Annalen, Vol. 336, No. 4
  - Zeta functions of line, middle, total graphs of a graph and their coverings
    Jin Ho Kwak and Iwao Sato
    1 Oct 2006 | Linear Algebra and its Applications, Vol. 418, No. 1
  - A discrete Lefschetz formula
    Anton Deitmar
    1 Aug 2006 | Topology and its Applications, Vol. 153, No. 14
  - Weighted Bartholdi zeta functions of graphs
    Iwao Sato
    1 Jul 2006 | European Journal of Combinatorics, Vol. 27, No. 5
  - L-functions for line graphs of semiregular bipartite graphs
    Iwao Sato
    1 Jul 2006 | Linear Algebra and its Applications, Vol. 416, No. 2-3
  - THE IHARA–SELBERG ZETA FUNCTION FOR PGL3 AND HECKE OPERATORS
    ANTON DEITMAR
    and
    J. WILLIAM HOFFMAN
    25 January 2012 | International Journal of Mathematics, Vol. 17, No. 02
  - Bartholdi zeta functions of some graphs
    Hirobumi Mizuno and Iwao Sato
    1 Feb 2006 | Discrete Mathematics, Vol. 306, No. 2
  - A New Proof of Bartholdi's Theorem
    Hirobumi Mizuno and Iwao Sato
    1 Nov 2005 | Journal of Algebraic Combinatorics, Vol. 22, No. 3
  - Zeta functions of oriented line graphs of graph coverings
    Hirobumi Mizuno and Iwo Sato
    1 Nov 2005 | Discrete Mathematics, Vol. 303, No. 1-3
  - Functionals of Brownian motion, localization and metric graphs
    Alain Comtet, Jean Desbois and Christophe Texier
    31 August 2005 | Journal of Physics A: Mathematical and General, Vol. 38, No. 37
  - Bartholdi zeta functions of graph bundles having regular fibers
    Jin Ho Kwak, Jaeun Lee and Moo Young Sohn
    1 Jul 2005 | European Journal of Combinatorics, Vol. 26, No. 5
  - Bartholdi zeta functions of line graphs and middle graphs of graph coverings
    Hirobumi Mizuno and Iwao Sato
    1 Mar 2005 | Discrete Mathematics, Vol. 292, No. 1-3
  - The number of spanning forests of a graph
    Yasuo Teranishi
    1 Feb 2005 | Discrete Mathematics, Vol. 290, No. 2-3
  - Weighted zeta functions of graphs
    Hirobumi Mizuno and Iwao Sato
    1 Jul 2004 | Journal of Combinatorial Theory, Series B, Vol. 91, No. 2
  - Combinatorics of the Two-Variable Zeta Function
    Iwan M. Duursma
    1 Jan 2004
  - Bartholdi zeta functions of digraphs
    Hirobumi Mizuno and Iwao Sato
    1 Nov 2003 | European Journal of Combinatorics, Vol. 24, No. 8
  - On the weighted complexity of a regular covering of a graph
    Hirobumi Mizuno and Iwao Sato
    1 Sep 2003 | Journal of Combinatorial Theory, Series B, Vol. 89, No. 1
  - Bartholdi zeta functions of graph coverings
    Hirobumi Mizuno and Iwao Sato
    1 Sep 2003 | Journal of Combinatorial Theory, Series B, Vol. 89, No. 1
  - L-functions of regular coverings of graphs
    Hirobumi Mizuno and Iwao Sato
    1 Apr 2003 | European Journal of Combinatorics, Vol. 24, No. 3
  - The semicircle law for semiregular bipartite graphs
    Hirobumi Mizuno and Iwao Sato
    1 Feb 2003 | Journal of Combinatorial Theory, Series A, Vol. 101, No. 2
  - Good Expander Graphs and Expander Codes: Parameters and Decoding
    H. Janwa
    30 April 2003
  - Weighted zeta functions of digraphs
    Hirobumi Mizuno and Iwao Sato
    1 Nov 2002 | Linear Algebra and its Applications, Vol. 355, No. 1-3
  - Zeta functions of digraphs
    Hirobumi Mizuno and Iwao Sato
    1 Oct 2001 | Linear Algebra and its Applications, Vol. 336, No. 1-3
  - A Polya-Hilbert operator for automorphic L-functions
    Anton Deitmar
    1 Jun 2001 | Indagationes Mathematicae, Vol. 12, No. 2
  - Zeta Functions of Discrete Groups Acting on Trees
    Bryan Clair and Shahriar Mokhtari-Sharghi
    1 Mar 2001 | Journal of Algebra, Vol. 237, No. 2
  - Ramanujan Edge-Indexed Graphs
    Shahriar Mokhtari-Sharghi
    1 Mar 2001 | Journal of Combinatorial Theory, Series B, Vol. 81, No. 2
  - Zeta Functions of Graph Coverings
    Hirobumi Mizuno and Iwao Sato
    1 Nov 2000 | Journal of Combinatorial Theory, Series B, Vol. 80, No. 2
  - Zeta Functions of Finite Graphs and Coverings, Part II
    H.M. Stark and A.A. Terras
    1 Sep 2000 | Advances in Mathematics, Vol. 154, No. 1
  - Combinatorial L2 -determinants
    Anton Deitmar
    20 January 2009 | Proceedings of the Edinburgh Mathematical Society, Vol. 43, No. 1
  - Two Proofs of Ihara’s Theorem
    Sam Northshield
    1 Jan 1999
  - Multipath Zeta Functions of Graphs
    Harold M. Stark
    1 Jan 1999
  - Спектральная задача на графах и $L$-функции
    Леонид Олегович Чехов and Leonid Olegovich Chekhov
    1 Jan 1999 | Успехи математических наук, Vol. 54, No. 6
  - Ihara Zeta Functions for Periodic Simple Graphs
    Daniele Guido, Tommaso Isola and Michel L. Lapidus
  - Panorama of Zeta Functions
    Anton Deitmar
- Recommended
Vol. 03, No. 06
Metrics
Downloaded 193 times

History

Received 6 May 1992
Keywords
Loading ...

System Upgrade on Feb 12th

THE IHARA-SELBERG ZETA FUNCTION OF A TREE LATTICE

Recommended