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On the basis problem for Siegel-Hilbert modular forms


Author: Jinghua Kuang
Journal: Bull. Amer. Math. Soc. 25 (1991), 61-67
MSC (1985): Primary 11F41, 11F27
DOI: https://doi.org/10.1090/S0273-0979-1991-16025-8
MathSciNet review: 1090405
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  • Armand Borel and Harish-Chandra, Arithmetic subgroups of algebraic groups, Ann. of Math. (2) 75 (1962), 485–535. MR 0147566, https://doi.org/10.2307/1970210
  • Siegfried Böcherer, Siegel modular forms and theta series, Theta functions—Bowdoin 1987, Part 2 (Brunswick, ME, 1987) Proc. Sympos. Pure Math., vol. 49, Amer. Math. Soc., Providence, RI, 1989, pp. 3–17. MR 1013165
  • M. Eichler, The basis problem for modular forms and the traces of the Hecke operators, Modular functions of one variable, I (Proc. Internat. Summer School, Univ. Antwerp, Antwerp, 1972) Springer, Berlin, 1973, pp. 75–151. Lecture Notes in Math., Vol. 320. MR 0485698
    M. Eichler, Correction to: “The basis problem for modular forms and the traces of the Hecke operators” (Modular functions of one variable, I (Proc. Internat. Summer School, Univ. Antwerp, 1972), pp. 75–151, Lecture Notes in Math., Vol. 320, Springer, Berlin, 1973), Modular functions of one variable, IV (Proc. Internat. Summer School, Univ. Antwerp, Antwerp, 1972) Springer, Berlin, 1975, pp. 145–147. Lecture Notes in Math., Vol. 476. MR 0485699
  • [Fi] T. Finnegan, Siegel-Hilbert modular forms of level one over fields with narrow class number one are theta series, Ph.D. thesis, University of Minnesota, 1989.
  • E. Freitag, Stabile Modulformen, Math. Ann. 230 (1977), no. 3, 197–211 (German). MR 0481144, https://doi.org/10.1007/BF01367576
  • [Ga1] P. B. Garrett, Fullbacks of Eisenstein series, applications, Automorphic Forms of Several Variables, Taniguchi Symposium, Katata, 1983, Birkhäuser.
  • Paul B. Garrett, Arithmetic properties of Fourier-Jacobi expansions of automorphic forms in several variables, Amer. J. Math. 103 (1981), no. 6, 1103–1134. MR 636954, https://doi.org/10.2307/2374226
  • Erich Hecke, Mathematische Werke, Herausgegeben im Auftrage der Akademie der Wissenschaften zu Göttingen, Vandenhoeck & Ruprecht, Göttingen, 1959 (German). MR 0104550
  • Hiroaki Hijikata, Arnold K. Pizer, and Thomas R. Shemanske, The basis problem for modular forms on Γ₀(𝑁), Mem. Amer. Math. Soc. 82 (1989), no. 418, vi+159. MR 960090, https://doi.org/10.1090/memo/0418
  • Helmut Klingen, Introductory lectures on Siegel modular forms, Cambridge Studies in Advanced Mathematics, vol. 20, Cambridge University Press, Cambridge, 1990. MR 1046630
  • Martin Kneser, Strong approximation, Algebraic Groups and Discontinuous Subgroups (Proc. Sympos. Pure Math., Boulder, Colo., 1965) Amer. Math. Soc., Providence, R.I., 1966, pp. 187–196. MR 0213361
  • [Ku] J. Kuang, Certain Siegel-Hilbert modular forms of higher square-free levels are representable as theta series, Ph.D. Thesis, University of Minnesota, 1991.
  • Michio Ozeki, On basis problem for Siegel modular forms of degree 2, Acta Arith. 31 (1976), no. 1, 17–30. MR 0432553
  • Ichirô Satake, Theory of spherical functions on reductive algebraic groups over 𝔭-adic fields, Inst. Hautes Études Sci. Publ. Math. 18 (1963), 5–69. MR 0195863
  • Jean-Pierre Serre, Trees, Springer-Verlag, Berlin-New York, 1980. Translated from the French by John Stillwell. MR 607504
  • Goro Shimura, On the Fourier coefficients of modular forms of several variables, Nachr. Akad. Wiss. Göttingen Math.-Phys. Kl. II 17 (1975), 261–268. MR 0485706
  • J.-L. Waldspurger, Engendrement par des séries thêta de certains espaces de formes modulaires, Invent. Math. 50 (1978/79), no. 2, 135–168 (French). MR 517775, https://doi.org/10.1007/BF01390287
  • André Weil, Sur la formule de Siegel dans la théorie des groupes classiques, Acta Math. 113 (1965), 1–87 (French). MR 0223373, https://doi.org/10.1007/BF02391774
  • André Weil, Sur la formule de Siegel dans la théorie des groupes classiques, Acta Math. 113 (1965), 1–87 (French). MR 0223373, https://doi.org/10.1007/BF02391774
  • Rainer Weissauer, Stabile Modulformen und Eisensteinreihen, Lecture Notes in Mathematics, vol. 1219, Springer-Verlag, Berlin, 1986 (German). MR 923958

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DOI: https://doi.org/10.1090/S0273-0979-1991-16025-8