Duke Mathematical Journal

An exact mass formula for orthogonal groups

Goro Shimura

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Article information

Duke Math. J., Volume 97, Number 1 (1999), 1-66.

First available in Project Euclid: 19 February 2004

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 11F55: Other groups and their modular and automorphic forms (several variables)
Secondary: 11E12: Quadratic forms over global rings and fields


Shimura, Goro. An exact mass formula for orthogonal groups. Duke Math. J. 97 (1999), no. 1, 1--66. doi:10.1215/S0012-7094-99-09701-6. https://projecteuclid.org/euclid.dmj/1077228500

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  • [E1] Martin Eichler, Die Ähnlichkeitsklassen indefiniter Gitter, Math. Z. 55 (1952), 216–252.
  • [E2] Martin Eichler, Quadratische Formen und orthogonale Gruppen, Springer-Verlag, Berlin, 1974, 2d ed., Grundlehren Math. Wiss. 63.
  • [K] Martin Kneser, Klassenzahlen indefiniter quadratischer Formen in drei oder mehr Veränderlichen, Arch. Math. (Basel) 7 (1956), 323–332.
  • [M] L. J. Mordell, The definite quadratic forms in eight variables with determinant unity, J. Math. Pures Appl. 17 (1938), no. 9, 41–46.
  • [S1] Goro Shimura, Confluent hypergeometric functions on tube domains, Math. Ann. 260 (1982), no. 3, 269–302.
  • [S2] Goro Shimura, On Eisenstein series, Duke Math. J. 50 (1983), no. 2, 417–476.
  • [S3] Goro Shimura, On the transformation formulas of theta series, Amer. J. Math. 115 (1993), no. 5, 1011–1052.
  • [S4] Goro Shimura, Euler products and Fourier coefficients of automorphic forms on symplectic groups, Invent. Math. 116 (1994), no. 1-3, 531–576.
  • [S5] Goro Shimura, Euler products and Eisenstein series, CBMS Regional Conference Series in Mathematics, vol. 93, Published for the Conference Board of the Mathematical Sciences, Washington, DC, 1997, Amer. Math. Soc., Providence.
  • [S6] Goro Shimura, Zeta functions and Eisenstein series on classical groups, Proc. Nat. Acad. Sci. U.S.A. 94 (1997), no. 21, 11133–11137, in Elliptic Curves and Modular Forms (Washington, D.C., 1996).
  • [Si]1 Carl Ludwig Siegel, Gesammelte Abhandlungen. Bände I, II, III, Herausgegeben von K. Chandrasekharan und H. Maass, Springer-Verlag, Berlin, 1966.
  • [Si]2 Carl Ludwig Siegel, Gesammelte Abhandlungen. Band IV, Springer-Verlag, Berlin, 1979.