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A Generalization of Epstein’s Zeta Function

Published online by Cambridge University Press:  22 January 2016

Audrey Terras
Audrey Terras*
Affiliation:
University of Illinois, Urbana, Illinois
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Koecher defined in [3] the following zeta function associated with the matrix S(n) of a positive quadratic form and one complex variable ρ

(1)

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 42 , March 1971 , pp. 173 - 188
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1971

References

[1] Helgason, S., Differential Geometry and Symmetric Spaces. New York, Academic Press, 1962.Google Scholar
[2] Hörmander, Lars, An Introduction to Complex Analysis in Several Variables. Princeton, N.J.D. Van Nostrand, 1966.Google Scholar
[3] Koecher, Max, “Über Dirichlet-Reihen mit Funktionalgleichung,” J. Reine Angew. Math. 192 (1953), 1–23.CrossRefGoogle Scholar
[4] Maass, H., “Some Remarks on Selberg’s Zeta Functions”, Proc. Internatl. Conf. on Several Complex Variables, U. of Maryland, College Park, Md. 1970.Google Scholar
[5] Selberg, A., “Harmonic Analysis and Discontinuous Groups in Weakly Symmetric Riemannian Spaces with Applications to Dirichlet Series,” J. Indian Math. Soc. (1956), 47–87.Google Scholar
[6] Selberg, A., “A New Type of Zeta Function Connected with Quadratic Forms”, Report of the Inst. in Theory of Numbers, U. of Colorado, Boulder, Colo. 1959, 207–210.Google Scholar
[7] Selberg, A., “Discontinuous Groups and Harmonic Analysis”, Proc. Internatl. Cong, of Math., Stockholm, 1962, 177–189.Google Scholar
[8] Siegel, C.L., Gesammelte Abhandlungen, New York, Springer Verlag, 1966.CrossRefGoogle Scholar
[9] Terras, A., “A Generalization of Epstein’s Zeta Function”, Ph.D. Thesis, Yale, New Haven, Conn., 1970.Google Scholar