On zeta-functions of infinite-dimensional representations
Sbornik. Mathematics, Tome 21 (1973) no. 4, pp. 499-509
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In this paper we consider the group of similitudes of a nondegenerate symmetric or antisymmetric bilinear form over a global field. For representations of this group, realized as functions on the factor-space of the adèles of this group modulo the principal adèles, we construct certain zeta-functions possessing an Euler product and a meromorphic continuation. Bibliography: 7 titles.
@article{SM_1973_21_4_a0,
author = {M. E. Novodvorskii and I. I. Pyatetskii-Shapiro},
title = {On~zeta-functions of infinite-dimensional representations},
journal = {Sbornik. Mathematics},
pages = {499--509},
year = {1973},
volume = {21},
number = {4},
language = {en},
url = {http://geodesic.mathdoc.fr/item/SM_1973_21_4_a0/}
}
M. E. Novodvorskii; I. I. Pyatetskii-Shapiro. On zeta-functions of infinite-dimensional representations. Sbornik. Mathematics, Tome 21 (1973) no. 4, pp. 499-509. http://geodesic.mathdoc.fr/item/SM_1973_21_4_a0/
[1] N. Burbaki, Algebra. Moduli, koltsa, formy, izd-vo «Nauka», Moskva, 1966 | MR
[2] T. A. Springer, R. Steinberg, Conjugacy classes, Lect. notes in math., 131, 1970 | MR
[3] A. Borel, Lineinye algebraicheskie gruppy, izd-vo «Mir», Moskva, 1972 | MR
[4] G. Harder, “Minkowskische Reduktiontheorie über Funktionenkörpern”, Invent. Math., 7 (1969), 33–54 | DOI | MR | Zbl
[5] R. P. Langlands, “Eisenstein series”, Proc. simp. Pure Math., IX, Providence, 1966 | MR
[6] I. M. Gelfand, M. I. Graev, I. I. Pyatetskii-Shapiro, Teoriya predstavlenii i avtomorfnye funktsii, izd-vo «Nauka», Moskva, 1966 | MR
[7] M. E. Novodvorskii, “O teoremakh edinstvennosti obobschennykh modelei Besselya”, Matem. sb., 90 (132) (1973), 275–287 | MR | Zbl