𝐿-functions of 2×2 unitary groups and factorization of periods of Hilbert modular forms

Harris, Michael

Journal of the American Mathematical Society, Tome 06 (1993) no. 3, pp. 637-719

Détail

DOI : 10.1090/S0894-0347-1993-1186960-7

Bibliographie

[1] Blasius, Don On the critical values of Hecke 𝐿-series Ann. of Math. (2) 1986 23 63

[2] Borovoĭ, M. V. Langlands’ conjecture concerning conjugation of connected Shimura varieties Selecta Math. Soviet. 1983/84 3 39

[3] Deligne, Pierre, Milne, James S., Ogus, Arthur, Shih, Kuang-Yen Hodge cycles, motives, and Shimura varieties 1982

[4] Garrett, Paul B., Harris, Michael Special values of triple product 𝐿-functions Amer. J. Math. 1993 161 240

[5] Gelbart, Stephen, Piatetski-Shapiro, Ilya, Rallis, Stephen Explicit constructions of automorphic 𝐿-functions 1987

[6] Gelbart, Stephen S., Rogawski, Jonathan D. 𝐿-functions and Fourier-Jacobi coefficients for the unitary group 𝑈(3) Invent. Math. 1991 445 472

[7] Harris, Michael Arithmetic vector bundles and automorphic forms on Shimura varieties. I Invent. Math. 1985 151 189

[8] Freitag, Eberhard Hilbert modular forms 1990

[9] Harris, Michael, Kudla, Stephen S. Arithmetic automorphic forms for the nonholomorphic discrete series of 𝐺𝑆𝑝(2) Duke Math. J. 1992 59 121

[10] Harris, Michael, Kudla, Stephen S. The central critical value of a triple product 𝐿-function Ann. of Math. (2) 1991 605 672

[11] Howe, R. 𝜃-series and invariant theory 1979 275 285

[12] Howe, Roger Transcending classical invariant theory J. Amer. Math. Soc. 1989 535 552

[13] Jacquet, Hervé Automorphic forms on 𝐺𝐿(2). Part II 1972

[14] Jacquet, H., Langlands, R. P. Automorphic forms on 𝐺𝐿(2) 1970

[15] Jannsen, Uwe Mixed motives and algebraic 𝐾-theory 1990

[16] Kashiwara, M., Vergne, M. On the Segal-Shale-Weil representations and harmonic polynomials Invent. Math. 1978 1 47

[17] Kudla, Stephen S. On certain arithmetic automorphic forms for 𝑆𝑈(1,𝑞) Invent. Math. 1979 1 25

[18] Kudla, Stephen S. Seesaw dual reductive pairs 1984 244 268

[19] Kudla, Stephen S., Rallis, Stephen On the Weil-Siegel formula J. Reine Angew. Math. 1988 1 68

[20] Kudla, Stephen S., Rallis, Stephen Poles of Eisenstein series and 𝐿-functions 1990 81 110

[21] Labesse, J.-P., Langlands, R. P. 𝐿-indistinguishability for 𝑆𝐿(2) Canadian J. Math. 1979 726 785

[22] Milne, J. S. Canonical models of (mixed) Shimura varieties and automorphic vector bundles 1990 283 414

[23] Mœglin, Colette, Vignéras, Marie-France, Waldspurger, Jean-Loup Correspondances de Howe sur un corps 𝑝-adique 1987

[24] Oda, Takayuki Periods of Hilbert modular surfaces 1982

[25] Oda, Takayuki Hodge structures of Shimura varieties attached to the unit groups of quaternion algebras 1983 15 36

[26] Piatetski-Shapiro, I., Rallis, S. 𝜀 factor of representations of classical groups Proc. Nat. Acad. Sci. U.S.A. 1986 4589 4593

[27] Prasad, Dipendra Trilinear forms for representations of 𝐺𝐿(2) and local 𝜀-factors Compositio Math. 1990 1 46

[28] Rallis, Stephen 𝐿-functions and the oscillator representation 1987

[29] Shimizu, Hideo Theta series and automorphic forms on 𝐺𝐿₂ J. Math. Soc. Japan 1972 638 683

[30] Shimura, Goro On canonical models of arithmetic quotients of bounded symmetric domains Ann. of Math. (2) 1970 144 222

[31] Shimura, Goro The special values of the zeta functions associated with Hilbert modular forms Duke Math. J. 1978 637 679

[32] Shimura, Goro Automorphic forms and the periods of abelian varieties J. Math. Soc. Japan 1979 561 592

[33] Shimura, Goro The arithmetic of certain zeta functions and automorphic forms on orthogonal groups Ann. of Math. (2) 1980 313 375

[34] Shimura, Goro The critical values of certain zeta functions associated with modular forms of half-integral weight J. Math. Soc. Japan 1981 649 672

[35] Shimura, Goro Algebraic relations between critical values of zeta functions and inner products Amer. J. Math. 1983 253 285

[36] Shimura, Goro On the critical values of certain Dirichlet series and the periods of automorphic forms Invent. Math. 1988 245 305

[37] Tunnell, Jerrold B. Local 𝜀-factors and characters of 𝐺𝐿(2) Amer. J. Math. 1983 1277 1307

[38] Waldspurger, J.-L. Démonstration d’une conjecture de dualité de Howe dans le cas 𝑝-adique, 𝑝≠2 1990 267 324

[39] Waldspurger, J.-L. Quelques propriétés arithmétiques de certaines formes automorphes sur 𝐺𝐿(2) Compositio Math. 1985 121 171

[40] Waldspurger, J.-L. Quelques propriétés arithmétiques de certaines formes automorphes sur 𝐺𝐿(2) Compositio Math. 1985 121 171

[41] Waldspurger, Jean-Loup Correspondances de Shimura et quaternions Forum Math. 1991 219 307

[42] Weil, André Sur la formule de Siegel dans la théorie des groupes classiques Acta Math. 1965 1 87

[43] Rallis, S. On the Howe duality conjecture Compositio Math. 1984 333 399