Divisor of the Selberg zeta function for kleinian groups
Journées équations aux dérivées partielles, (1994), p. 1-9
@article{JEDP_1994____A8_0,
     author = {Perry, Peter},
     title = {Divisor of the Selberg zeta function for kleinian groups},
     journal = {Journ\'ees \'equations aux d\'eriv\'ees partielles},
     publisher = {Ecole polytechnique},
     year = {1994},
     pages = {1-9},
     zbl = {0871.11056},
     mrnumber = {1298679},
     language = {en},
     url = {http://www.numdam.org/item/JEDP_1994____A8_0}
}
Perry, Peter A. Divisor of the Selberg zeta function for kleinian groups. Journées équations aux dérivées partielles,  (1994), pp. 1-9. https://www.numdam.org/item/JEDP_1994____A8_0/

[1] S. Agmon. On the spectral theory of the Laplacian on non-compact hyperbolic manifolds. Journées « Équations aux dérivées partielles » (Saint Jean de Monts, 1987), Exposée No. XVII, École Polytechnique, Palaiseau, 1987. | Numdam | MR 89c:58128 | Zbl 0636.58037

[2] S. Agmon. On the representation theorem for solutions of the Helmholtz equation in hyperbolic space. Preprint, Forschungsinstitut für Mathematik, ETH-Zürich, 1990.

[3] Boas, R. P. Entire Functions. New York : Academic Press, 1954. | Zbl 0058.30201

[4] R. Bowen. Symbolic dynamics for hyperbolic flows, Amer. Math. J. 95 (1973), 429-460. | MR 49 #4041 | Zbl 0282.58009

[5] D. Fried. The zeta functions of Ruelle and Selberg, I, Ann. scient. Éc. Norm. Sup. 19 (1986), 491-517. | Numdam | MR 88k:58134 | Zbl 0609.58033

[6] R. Froese, P. Hislop, P. Perry. The Laplace operator on hyperbolic three-manifolds with cusps of non-maximal rank. Inventiones Math. 106 (1991), 295-333. | MR 93b:11065 | Zbl 0763.58028

[7] C. Gérard. Asymptotique des pôles de la matrice de scattering pour deux obstacles strictement convexes. Bulletin de la S.M.F. 116 (1988), Mémoire No. 31. | Numdam | Zbl 0654.35081

[8] L. Guillopé, M. Zworski. Upper bounds on the number of resonances for non-compact Riemann surfaces. Preprint, 1993. | Zbl 0841.58063

[9] L. Guillopé, M. Zworski. Polynomial bounds on the number of resonances for some complete spaces of constant negative curvature near infinity. Preprint, 1993. | Zbl 0859.58028

[10] M. Ikawa. On the poles of the scattering matrix for two strictly convex obstacles. J. Math. Kyoto Univ. 23 (1983), 127-194. | MR 84e:35118 | Zbl 0561.35060

[11] M. Ikawa. On the existence of poles of the scattering matrix for several convex bodies. Proc. Japan Acad. 64 (1988), 91-93. | MR 90i:35211 | Zbl 0704.35113

[12] P. Lax, R. S. Phillips. The asymptotic distribution of lattice points in Euclidean and non-Euclidean spaces. J. Funct. Anal. 46 (1982), 280-350. | MR 83j:10057 | Zbl 0497.30036

[13] P. Lax, R. S. Phillips. Translation representation for automorphic solutions of the non-Euclidean wave equation I, II, III. Comm. Pure. Appl. Math. 37 (1984), 303-328, 37 (1984), 779-813, and 38 (1985), 179-208. | Zbl 0549.10019

[14] P. Lax, R. S. Phillips. Translation representation for automorphic solutions of the non-Euclidean wave equation IV. Preprint, Stanford University, 1990.

[15] N. Mandouvalos. Scattering operator, Eisenstein series, inner product formula, and «Maass-Selberg» relations for Kleinian groups. Mem. Amer. Math. Soc. 400 (1989). | Zbl 0673.10023

[16] A. Manning. Axiom A difeomorphisms have rational zeta functions. Bull. London Math. Soc. 3 (1971), 215-220. | MR 44 #5982 | Zbl 0219.58007

[17] R. Mazzeo, R. Melrose. Meromorphic extension of the resolvent on complete spaces with asymptotically constant negative curvature. J. Funct. Anal. 75 (1987), 260-310. | MR 89c:58133 | Zbl 0636.58034

[18] S. J. Patterson. The Laplacian operator on a Riemann surface I, II, III. Compositio Math. 31 (1975), 83-107, 32 (1976) 71-112, and 33 (1976), 227-259. | Numdam | Zbl 0342.30011

[19] S. J. Patterson. The Selberg zeta-function of a Kleinian group. In Number Theory, Trace Formulas, and Discrete Groups : Symposium in honor of Atle Selberg, Oslo, Norway, July 14-21, 1987, New York, Academic Press, 1989, pp. 409-442. | Zbl 0668.10036

[20] S. J. Patterson. On Ruelle's zeta-function. In Festschrift in honor of I.I. Piatetski-Shapiro on the occasion of his sixtieth birthday, ed. S. Gelbart, R. Howe, P. Sarnak. Jerusalem : Weizmann Science Press, 1990. | MR 93d:58126 | Zbl 0721.58041

[21] S. J. Patterson, P. A. Perry. The divisor of the Selberg Zeta function for Kleinian groups, in preparation. | Zbl 01820780

[22] P. A. Perry. The Laplace operator on a hyperbolic manifold, II. Eisenstein series and the scattering matrix. J. reine angew. Math. 398 (1989), 67-91. | MR 90g:58138 | Zbl 0677.58044

[23] P. A. Perry. The Selberg zeta function and a local trace formula for Kleinian groups. J. reine angew. Math. 410 (1990), 116-152. | MR 92e:11057 | Zbl 0697.10027

[24] P. A. Perry. The Selberg zeta function and scattering poles for Kleinian groups. Bull. Amer. Math. Soc. 24 (1991), 327-333. | MR 92d:58213 | Zbl 0723.11028

[25] D. Ruelle. Zeta functions for expanding maps and Anosov flows, Inventiones Math. 34, (1976), 231-242. | MR 54 #8732 | Zbl 0329.58014

[26] A. Selberg. Harmonic analysis and discontinuous groups in weakly symmetric Riemannian spaces with applications to Dirichlet series. J. Indian Math. Soc. 20 (1956), 47-87. | MR 19,531g | Zbl 0072.08201