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Functional Equations of Generalized Epstein Zeta Functions in Several Complex Variables

Published online by Cambridge University Press:  22 January 2016

Audrey A. Terras
Audrey A. Terras*
Affiliation:
University of Illinois
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Let S(n) be the matrix of a positive definite quadratic form and

Define

1.

Here the sum is over unimodular matrices which lie in a complete set of representatives for the equivalence relation with P unimodular and having block form

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 44 , December 1971 , pp. 89 - 95
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1971

References

Blbliography

[1] Koecher, Max, “Uber Dirichlet-Reihen mit Funktionalgleichung”, J. Reine Angew. Math. 192 (1953), 1–23.Google Scholar
[2] Langlands, R.P., “Eisenstein Series”, Algebraic Groups and Discontinuous Subgroups, Proc. Symp. in Pure Math. IX, Providence, R.I., A.M.S., 1966.Google Scholar
[3] 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
[4] 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
[5] Selberg, A., “A New Type of Zeta Function Connected with Quadratic Forms”, Report of the Institute in Theory of Numbers, U. of Colorado, Boulder, Colo., 1959, 207–210.Google Scholar
[6] Selberg, A., “Discontinuous Groups and Harmonic Analysis”, Proc. Internati. Cong, of Math., Stockholm, 1962, 177–189 Google Scholar
[7] Terras, A., “A Generalization of Epstein’s Zeta Function”, Nagoya Math., J. 42 (1971),Google Scholar