Geodesic
Explicit duality formulas for symplectic and orthogonal Hecke operators on theta-series of positive quadratic forms
Sbornik. Mathematics, Tome 58 (1987) no. 2, pp. 417-434 Cet article a éte moissonné depuis la source Math-Net.Ru

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The Rallis mapping is used to obtain commutation formulas for the Hecke operators of the symplectic and orthogonal groups on the space of theta-series. These formulas are applied to the multiplicative arithmetic of representations of quadratic forms by forms. Bibliography: 15 titles. 
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     title = {Explicit duality formulas for symplectic and orthogonal {Hecke} operators on theta-series of positive quadratic forms},
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V. G. Zhuravlev. Explicit duality formulas for symplectic and orthogonal Hecke operators on theta-series of positive quadratic forms. Sbornik. Mathematics, Tome 58 (1987) no. 2, pp. 417-434. http://geodesic.mathdoc.fr/item/SM_1987_58_2_a7/

[1] Eichler M., Quadratische Formen und orthogonale Gruppen, Springer, Berlin, 1974 | MR | Zbl

[2] Andrianov A. N., “Operatory Gekke i predstavleniya binarnykh kvadratichnykh form”, Tr. MIAN, 165, 1984, 4–15 | MR | Zbl

[3] Andrianov A. N., “Predstavleniya chetnoi dzeta-funktsii na teta-ryadakh”, Zap. nauchn. seminarov LOMI, 134, 1984, 5–14 | MR | Zbl

[4] Veil A., “O nekotorykh gruppakh unitarnykh operatorov”, Matematika (sb. perevodov), 13:5 (1969), 33–94

[5] Howe R., “$\Theta$-series and invariant theory”, part 1, Proc. Symp. Pure Math., 33, Amer. Math. Soc., Providence, R.I., 1979, 275–285 | MR

[6] Rallis S., “The Eichler commutation relation and the continuous spectrum of the Weill representation”, Lecture notes in Math., 728, Springer, Berlin, 1979, 211–244 | MR

[7] Rallis S., “Langlands' functoriality and the Weil representation”, Amer. J. Math., 104 (1982), 465–515 | DOI | MR

[8] Andrianov A. N., Maloletkin G. N., “Povedenie teta-ryadov roda $n$ pri modulyarnykh podstanovkakh”, Izv. AN SSSR. Ser. matem., 39:2 (1975), 243–258 | MR | Zbl

[9] Andrianov A. N., “Multiplikativnaya arifmetika zigelevykh modulyarnykh form”, UMN, 34:1 (1979), 67–135 | MR | Zbl

[10] Shimura G., “Arithmetic of alternating forms and quaternion hermitian forms”, J. Math. Soc. Japan, 15 (1963), 33–65 | MR | Zbl

[11] Shimura G., Vvedenie v arifmetichekuyu teoriyu avtomorfnykh funktsii, Mir, M., 1973 | MR | Zbl

[12] Satake J., “Theory of spherical functions on reduetive algebraic group over $p$-adic fields”, Publ. Math. IHES, 1963, no. 18, 1–65 | MR

[13] Andrianov A. N., “Eilerovy razlozheniya teta-preobrazovanii zigelevykh modulyarnykh form roda $n$”, Matem. sb., 105(147) (1978), 291–341 | MR | Zbl

[14] Zhuravlev V. G., “Eilerovy razlozheniya teta-preobrazovanii zigelevykh modulyarnykh form polutselogo vesa i ikh analiticheskie svoistva”, Matem. sb., 123(165) (1984), 174–194 | MR | Zbl

[15] Andrianov A. N., “Ryady Dirikhle s eilerovskim proizvedenie v teorii zigelevykh modulyarnykh form roda 2”, Tr. MIAN, 112, 1971, 73–94 | MR | Zbl