Zeta functions of finite graphs and coverings

Advances in Mathematics

Volumn 121, Issue 1, 1996, Pages 124-165

  Stark, H M ^a   Terras, A A ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0030585874     PISSN: 00018708     EISSN: None     Source Type: Journal    
DOI: 10.1006/aima.1996.0050     Document Type: Article

References (17)

1. 1. H. BASS, The Ihara-Selberg zeta function of a tree lattice, Internat. J. Math. 3 (1992), 717-797.
2. 2. N. BIGGS, "Algebraic Graph Theory," Cambridge Univ. Press, Cambridge, 1993.
3. 3. H. DAVENPORT, "Multiplicative Number Theory," Springer-Verlag, New York, 1981.
4. 4. J. FRIEDMAN (Ed.), "Expanding Graphs," DIMACS Series in Discrete Math. and Theor. Comput. Sci., Vol. 10, Amer. Math. Soc., Providence, RI, 1993.
5. 5. K. HASHIMOTO, Zeta functions of finite graphs and representations of p-adic groups, Adv. Stud. Pure Math., Vol. 15, pp. 211-280, Academic Press, New York, 1989.
6. 6. K. HASHIMOTO, Artin-type L-functions and the density theorem for prime cycles on finite graphs, Internat. J. Math. 3 (1992), 809-826.
7. 7. Y. IHARA, On discrete subgroups of the two by two projective linear group over p-adic fields, J. Math. Soc. Japan 18 (1966), 219-235.
8. 8. S. LANG, "Algebraic Number Theory," Addison-Wesley, Reading, MA, 1968.
9. 9. A. LUBOTZKY, R. PHILLIPS, AND P. SARNAK, Ramanujan graphs, Combinatorica 8 (1988), 261-277.
10. 10. W. MASSEY, "Algebraic Topology: An Introduction," Springer-Verlag, New York, 1967.
11. 11. D. RUELLE, "Dynamical Zeta Functions for Piecewise Monotone Maps of the Interval," CRM Monograph Series, Vol. 4, Amer. Math. Soc., Providence, RI, 1994.
12. 12. J.-P. SERRE, "Trees," Springer-Verlag, New York, 1980.
13. 13. S. LYANAGA AND Y. KAWADA (Eds.), "Encyclopedic Dictionary of Mathematics," Vol. II, pp. 1372-1393, MIT Press, Cambridge, MA, 1977.
14. 14. T. SUNADA, L-functions in geometry and some applications, in "Lecture Notes in Math.," Vol. 2001, pp. 266-284, Springer-Verlag, New York, 1986.
15. 15. T. SUNADA, Fundamental groups and Laplacians, in "Lecture Notes in Math.," Vol. 1339, pp. 248-277, Springer-Verlag, New York, 1988.
16. 16. C. TRIMBLE, Ph.D. thesis, University of California, San Diego, 1993.
17. 17. A. B. VENKOV AND A. M. NIKITIN, The Selberg trace formula, Ramanujan graphs and some problems of mathematical physics, Petersburg Math. J. 5, No. 3 (1994), 419-484.