Selberg's trace formula on the k-regular tree and applications

International Journal of Mathematics and Mathematical Sciences

Volumn 2003, Issue 8, 2003, Pages 501-526

  Terras, Audrey ^a   Wallace, Dorothy ^b  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b Dartmouth College   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 17844408404     PISSN: 01611712     EISSN: None     Source Type: Journal    
DOI: 10.1155/S016117120311126X     Document Type: Article

References (27)

1. G. Ahumada, Fonctions périodiques et formule des traces de Selberg sur les arbres [Periodic functions and the Selberg trace formula for trees], C. R. Acad. Sci. Paris Sér. I Math. 305 (1987), no. 16, 709-712 (French). MathSciNet. Zentralblatt für Mathematik.
2. H. Bass, The Ihara-Selberg zeta function of a tree lattice, Int. J. Math. 3 (1992), no. 6, 717-797. MathSciNet. Zentralblatt für Mathematik.
3. R. Brooks, The spectral geometry of $k$-regular graphs, J. Anal. Math. 57 (1991), 120-151. MathSciNet. Zentralblatt für Mathematik.
4. P. Buser, Geometry and Spectra of Compact Riemann Surfaces, Progress in Mathematics, vol. 106, Birkhäuser Boston, Massachusetts, 1992. MathSciNet. Zentralblatt für Mathematik.
5. P. Cartier, Harmonic analysis on trees, Harmonic Analysis on Homogeneous Spaces (Proc. Sympos. Pure Math., Vol. 26, Williams Coll., Williamstown, Mass., 1972), American Mathematical Society, Rhode Island, 1973, pp. 419-424. MathSciNet. Zentralblatt für Mathematik.
6. A. Erdélyi, W. Magnus, F. Oberhettinger, and F. G. Tricomi, Higher Transcendental Functions. Vol. II, McGraw-Hill, New York, 1953. MathSciNet. Zentralblatt für Mathematik.
7. A. Figà-Talamanca and C. Nebbia, Harmonic Analysis and Representation Theory for Groups Acting on Homogeneous Trees, London Mathematical Society Lecture Note Series, vol. 162, Cambridge University Press, Cambridge, 1991. MathSciNet.
8. C. Gordon, D. Webb, and S. Wolpert, Isospectral plane domains and surfaces via Riemannian orbifolds, Invent. Math. 110 (1992), no. 1, 1-22. MathSciNet. Zentralblatt für Mathematik.
9. K.-I. Hashimoto, Zeta functions of finite graphs and representations of $p$-adic groups, Automorphic Forms and Geometry of Arithmetic Varieties, Advanced Studies in Pure Mathematics, vol. 15, Academic Press, Massachusetts, 1989, pp. 211-280. MathSciNet. Zentralblatt für Mathematik.
10. D. A. Hejhal, J. Friedman, M. C. Gutzwiller, and A. M. Odlyzko (eds.), Emerging Applications of Number Theory, The IMA Volumes in Mathematics and Its Applications, vol. 109, Springer-Verlag, New York, 1999. MathSciNet. Zentralblatt für Mathematik.
11. N. E. Hurt, Quantum Chaos and Mesoscopic Systems. Mathematical Methods in the Quantum Signatures of Chaos, Mathematics and Its Applications, vol. 397, Kluwer Academic Publishers, Dordrecht, 1997. MathSciNet. Zentralblatt für Mathematik.
12. 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. MathSciNet. Zentralblatt für Mathematik.
13. N. M. Katz and P. Sarnak, Zeroes of zeta functions and symmetry, Bull. Amer. Math. Soc. (N.S.) 36 (1999), no. 1, 1-26. CrossRef. MathSciNet. Zentralblatt für Mathematik.
14. A. Lubotzky, R. Phillips, and P. Sarnak, Ramanujan graphs, Combinatorica 8 (1988), no. 3, 261-277. MathSciNet. Zentralblatt für Mathematik.
15. G. Quenell, Spectral diameter estimates for $k$-regular graphs, Adv. Math. 106 (1994), no. 1, 122-148. CrossRef. MathSciNet. Zentralblatt für Mathematik.
16. A. Seiberg, Harmonic analysis and discontinuous groups in weakly symmetric Riemannian spaces with applications to Dirichlet series, J. Indian Math. Soc. (N.S.) 20 (1956), 47-87. MathSciNet. Zentralblatt für Mathematik.
17. H. M. Stark and A. A. Terras, Zeta functions of finite graphs and coverings, Adv. Math. 121 (1996), no. 1, 124-165. CrossRef. MathSciNet. Zentralblatt für Mathematik.
18. H. M. Stark and A. A. Terras, Zeta functions of finite graphs and coverings. II, Adv. Math. 154 (2000), no. 1, 132-195. CrossRef. MathSciNet. Zentralblatt für Mathematik.
19. T. Sunada, Fundamental groups and Laplacians, Geometry and Analysis on Manifolds (Katata/Kyoto, 1987), Lecture Notes in Mathematics, vol. 1339, Springer, Berlin, 1988, pp. 248-277. MathSciNet. Zentralblatt für Mathematik.
20. A. Terras, Harmonic Analysis on Symmetric Spaces and Applications. I, Springer-Verlag, New York, 1985. MathSciNet. Zentralblatt für Mathematik.
21. A. Terras, Fourier Analysis on Finite Groups and Applications, London Mathematical Society Student Texts, vol. 43, Cambridge University Press, Cambridge, 1999. MathSciNet. Zentralblatt für Mathematik.
22. A. Terras, Statistics of graph spectra for some finite matrix groups: finite quantum chaos, Special Functions (Hong Kong, 1999) (C. Dunkl et al., eds.), World Scientific Publishing, New Jersey, 2000, pp. 351-374. MathSciNet.
23. A. Terras, Finite quantum chaos, Amer. Math. Monthly 109 (2002), no. 2, 121-139. MathSciNet.
24. A. B. Venkov and A. M. Nikitin, The Selberg trace formula, Ramanujan graphs and some problems in mathematical physics, Algebra i Analiz 5 (1993), no. 3, 1-76 (Russian), translated in St. Petersburg Math. J. 5 (1994), no. 3, 419-484. MathSciNet. Zentralblatt für Mathematik.
25. A. B. Venkov and A. M. Nikitin, The Selberg trace formula, Ramanujan graphs and some problems in mathematical physics, Algebra i Analiz 5 (1993), no. 3, 1-76 (Russian), translated in St. Petersburg Math. J. 5 (1994), no. 3, 419-484. MathSciNet. Zentralblatt für Mathematik.
26. D. I. Wallace, Ergodic properties of quotients of horocycle flows on the Poincaré upper half plane, J. Math. Systems Estim. Control 8 (1998), no. 2, 193-196. Zentralblatt für Mathematik.
27. H. S. Wilf, Generatingfunctionology, Academic Press, Massachusetts, 1990. MathSciNet. Zentralblatt für Mathematik.