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References
Bochner, S.: On Riemann's functional equation with multiple gamma factors. Ann. Math.67, 29–41 (1958)
Bump, D.: The Rankin-Selberg method: a survey. In: Number theory, trace formula, and discrete groups, pp. 49–109. Aubert, K.E. et al. (eds.) London: Academic Press 1989
Conrey, J.B., Ghosh, A.: On the Selberg class of Dirichlet series: small weights. Preprint (1991)
Cramér, H.: Studien über die Nullstellen der Riemannschen Zetafunktion. Math. Z.4, 104–130 (1919)
Deninger, C.: LocalL-factors of motives and regularized products. Invent. Math.107, 135–150 (1992)
D'Hoker, E., Phong, D.: On determinants of Laplacians on Riemann surfaces. Commun. Math. Phys.105, 537–545 (1986)
Efrat, I.: Determinants of Laplacians on surfaces of finite volume. Commun. Math. Phys.119, 443–451 (1988)
Efrat, I.: Erratum: Determinants of Laplacians on surfaces of finite volume. Commun. Math. Phys.138, 607 (1991)
Gangolli, R.: Zeta functions of Selberg's type for compact space forms of symmetric space of rank one. III. J. Math.21, 1–42 (1977)
Gangolli, R., Warner, G.: Zeta functions of Selberg's type for some non-compact quotients of symmetric spaces of rank one. Nagoya Math. J.78, 1–44 (1980)
Gelbart, S., Shahidi, F.: Analytic properties of automorphicL-functions. San Diego: Academic Press 1988
Hejhal, D.A.: The Selberg trace formula forPSL(2,R), vol. 1 (Lect. Notes in Math., vol. 548. Berlin, Heidelberg, New York: Springer 1976
Hejhal, D.A.: The Selberg trace formula forPSL (2,R), vol. 2. (Lect. Notes Math., vol. 1001. Berlin Heidelberg, New York: 1983
Hermite, C.: Sur quelques points de la théorie des fonctions. J. Crelle91, 48–75 (1881) (Collected papers, vol. IV, pp. 48–75) Paris: Gauthier-Villiars 1917
Huxley, M.N.: Scattering matrices for congruence subgroups. In: Modular forms, pp. 157–196. Rankin, R.A. (ed.) New York: Wiley 1984
Illies, G.: Regularisierte Produkte und HeckescheL-Reihen. Preprint (1992)
Ingham, A.E.: The distribution of prime numbers. Cambridge: Cambridge University Press 1932
Jorgenson, J., Lang, S.: Complex analytic properties of regularized products. Yale University Preprin (1992), to appear Lect. Notes in Math.
Jorgenson, J., Lang, S.: A Parseval formula for functions with an asymptotic expansion at the origin. Yale University Preprint (1992), to appear Lect. Notes in Math.
Jorgenson, J., Lang, S.: Explicit formulas and regularized products. Yale University Preprint (1993)
Kaczorowski, J.: Thek-functions in multiplicative number theory. I. Acta Arith.56, 195–211 (1990)
Koyama, S.: Determinant expression of Selberg zeta functions. I. Trans. Am. Math. Soc.324, 149–168 (1991)
Koyama, S.: Determinant expression of Selberg zeta functions. III. Proc. Am. Math. Soc.113, 303–311 (1991)
Koyama, S.: Determinant expression of Selberg zeta functions. II. Trans. Am. Math. Soc.329, 755–772 (1992)
Kubota, T.: Elementary theory of Eisenstein series. New York: Wiley 1973
Kurokawa, N.: Parabolic components of zeta functions. Proc. Japan Acad. Ser. A64, 21–24 (1988)
Kurokawa, N.: Multiple sine functions and Selberg zeta functions. Proc. Japan Acad. Ser.A 67, 61–64 (1991)
Kurokawa, N.: Gamma factors and Plancherel measures. Proc. Japan Acad. Ser. A68, 256–260 (1992)
Lang, S.: Algebraic number theory. Menlo Park, CA.: Addison-Wesley 1970, reprinted as Grad. Texts Math., vol. 110. Berlin Heidelberg New York: Springer 1986
Lang, S.: Complex analysis. (Grad. Texts Math., vol 103. Berlin Heidelberg New York: Springer 1985, 3rd. edition 1993
Millson, J.: Closed geodesics and the η-invariant. Ann. Math.108, 1–39 (1978)
Moscovici, H., Stanton, R.J.: Eta invariants of Dirac operators on locally symmetric manifolds. Invent. Math.95, 629–666 (1989)
Sarnak, P.: Determinants of Laplacians. Commun. Math. Phys.110, 113–120 (1987)
Selberg, A.: Harmonic analysis and discontinuous groups in weakly symmetric Riemannian spaces with applications to Dirichlet series. J. Indian Math. Soc. B20, 47–87 (1956) (Collected papers volume I, pp. 423–463. Berlin Heidelberg New York: Springer 1989
Selberg, A.: Old and new conjectures and results about a class of Dirichlet series. Collected papers volume II, pp. 47–63. Berlin Heidelberg New York: Springer 1991
Serre, J.-P.: Facteurs locaux des fonctions zeta des variétés algébriques. Sem. Delange-Poitou-Pisot 1969–70, Exposé 19
Shimura, G.: Introduction to the arithmetic theory of automorphic functions. Princeton: Princeton University Press 1971
Vardi, I.: Determinants of Laplacians and multiple gamma functions. SISM J. Math. Anal.19, 493–507 (1988)
Vignéras, M.-F.: L'équation fonctionelle de la fonction zéta de Selberg du groupoe modulaireSL(2,Z). Astérisque61, 235–249 (1979)
Williams, F.L.: A factorization of the Selberg zeta function attached to a rank 1 space form. Manuscr. Math.77, 17–39 (1992)
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Actually the MSC does not, but should, include an item for regularized products. J.J. and S.L.
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Jorgenson, J., Lang, S. On Cramér's theorem for general Euler products with functional equation. Math. Ann. 297, 383–416 (1993). https://doi.org/10.1007/BF01459509
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DOI: https://doi.org/10.1007/BF01459509