On the basis problem for Siegel-Hilbert modular forms
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- by Jinghua Kuang PDF
- Bull. Amer. Math. Soc. 25 (1991), 61-67
References
- Armand Borel and Harish-Chandra, Arithmetic subgroups of algebraic groups, Ann. of Math. (2) 75 (1962), 485–535. MR 147566, DOI 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) Lecture Notes in Math., Vol. 320, Springer, Berlin, 1973, pp. 75–151. MR 0485698 [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 481144, DOI 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, DOI 10.2307/2374226
- Erich Hecke, Mathematische Werke, Vandenhoeck & Ruprecht, Göttingen, 1959 (German). Herausgegeben im Auftrage der Akademie der Wissenschaften zu Göttingen. MR 0104550
- Hiroaki Hijikata, Arnold K. Pizer, and Thomas R. Shemanske, The basis problem for modular forms on $\Gamma _0(N)$, Mem. Amer. Math. Soc. 82 (1989), no. 418, vi+159. MR 960090, DOI 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, DOI 10.1017/CBO9780511619878
- 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 432553, DOI 10.4064/aa-31-1-17-30
- Ichirô Satake, Theory of spherical functions on reductive algebraic groups over ${\mathfrak {p}}$-adic fields, Inst. Hautes Études Sci. Publ. Math. 18 (1963), 5–69. MR 195863, DOI 10.1007/BF02684781
- Jean-Pierre Serre, Trees, Springer-Verlag, Berlin-New York, 1980. Translated from the French by John Stillwell. MR 607504, DOI 10.1007/978-3-642-61856-7
- 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 485706
- 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, DOI 10.1007/BF01390287
- André Weil, Sur la formule de Siegel dans la théorie des groupes classiques, Acta Math. 113 (1965), 1–87 (French). MR 223373, DOI 10.1007/BF02391774
- André Weil, Sur la formule de Siegel dans la théorie des groupes classiques, Acta Math. 113 (1965), 1–87 (French). MR 223373, DOI 10.1007/BF02391774
- Rainer Weissauer, Stabile Modulformen und Eisensteinreihen, Lecture Notes in Mathematics, vol. 1219, Springer-Verlag, Berlin, 1986 (German). MR 923958, DOI 10.1007/BFb0072235
Additional Information
- 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