Geodesic
Zeta functions of parabolic forms
Sbornik. Mathematics, Tome 15 (1971) no. 4, pp. 619-641 
G. N. Maloletkin. Zeta functions of parabolic forms. Sbornik. Mathematics, Tome 15 (1971) no. 4, pp. 619-641. http://geodesic.mathdoc.fr/item/SM_1971_15_4_a8/
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Voir la notice de l'article provenant de la source Math-Net.Ru

It is shown that the zeta functions of parabolic forms for the multiplicative group of a simple algebra over a function field can be continued meromorphically, and a functional equation is obtained for such forms. Bibliography: 13 titles.

[1] A. N. Andrianov, “Dzeta-funktsii prostykh algebr s neabelevymi kharakterami”, Uspekhi matem. nauk, XXIII:4(142) (1968), 1–66 | MR

[2] I. M. Gelfand, M. I. Graev, I. I. Pyatetskii-Shapiro, Avtomorfnye formy i teoriya predstavlenii, Nauka, Moskva, 1966

[3] G. N. Maloletkin, “Dzeta-funktsii so sfericheskim kharakterom polnoi algebry matrits nad funktsionalnym polem”, Matem. zametki, 5:5 (1969), 577–586 | MR | Zbl

[4] I. R. Shafarevich, Dzeta-funktsiya, Nauka, Moskva, 1969

[5] K. Shevalle, Vvedenie v teoriyu algebraicheskikh funktsii ot odnoi peremennoi, IL, Moskva, 1956

[6] M. Deuring, Algebren, Chelsea, 1948 | Zbl

[7] R. Godement, “A theory of spherical functions”, Trans. Amer. Math. Soc., 73 (1952), 496–556 | DOI | MR | Zbl

[8] R. Godement, Les fonctions $\zeta$ des algebres simples, Sem. Bourbaki, 176, 1957/58

[9] R. Godement, Introduction á la théorie de Langlands, Sem. Bourbaki, 327, 1966/67

[10] G. Harder, “Minkowskische Reduktiontheorie über Funktionenkörpern”, Inv. Math., 7 (1969), 33–54 | DOI | MR | Zbl

[11] G. Harder, Chevolleygruppen uber Funktionenkorpern und automorphe Funktionen, Preprint | MR | Zbl

[12] J. Tate, “Fourier analysis in number fields und Hekke's zeta-functions”, Algebraic number theory, London–New York, 1967

[13] E. Witt, “Riemann–Rochscher Satz und $\zeta$-Funkion im Hyperkomplexen”, Math. Ann., 110 (1934), 12–28 | DOI | MR | Zbl