Geodesic
On zeta-functions of infinite-dimensional representations
Sbornik. Mathematics, Tome 21 (1973) no. 4, pp. 499-509 
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/
@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/}
}
TY  - JOUR
AU  - M. E. Novodvorskii
AU  - I. I. Pyatetskii-Shapiro
TI  - On zeta-functions of infinite-dimensional representations
JO  - Sbornik. Mathematics
PY  - 1973
SP  - 499
EP  - 509
VL  - 21
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/SM_1973_21_4_a0/
LA  - en
ID  - SM_1973_21_4_a0
ER  - 
%0 Journal Article
%A M. E. Novodvorskii
%A I. I. Pyatetskii-Shapiro
%T On zeta-functions of infinite-dimensional representations
%J Sbornik. Mathematics
%D 1973
%P 499-509
%V 21
%N 4
%U http://geodesic.mathdoc.fr/item/SM_1973_21_4_a0/
%G en
%F SM_1973_21_4_a0

Voir la notice de l'article provenant de la source Math-Net.Ru

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.

[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