The number of representations of an integer by a quadratic form
Goro Shimura
Source: Duke Math. J. Volume 100, Number 1 (1999), 59-92.
First Page PDF: View first page of article (PDF, 40 KB)Primary Subjects: 11E45
Secondary Subjects: 11E25, 11F27, 11F30
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Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.dmj/1077213844
Mathematical Reviews number (MathSciNet):
MR1714755
Zentralblatt MATH identifier:
01425252
Digital Object Identifier: doi:10.1215/S0012-7094-99-10002-0
References
[E] Martin Eichler, Quadratische Formen und orthogonale Gruppen, vol. 63, Springer-Verlag, Berlin, 1974, 2d ed.
Mathematical Reviews (MathSciNet):
MR50:4484
Zentralblatt MATH:
0277.10017
[KR] Stephen S. Kudla and Stephen Rallis, On the Weil-Siegel formula, J. Reine Angew. Math. 387 (1988), 1–68.
Mathematical Reviews (MathSciNet):
MR90e:11059
Zentralblatt MATH:
0644.10021
[R] Stephen Rallis, $L$-functions and the oscillator representation, Lecture Notes in Mathematics, vol. 1245, Springer-Verlag, Berlin, 1987.
Mathematical Reviews (MathSciNet):
MR89b:11046
Zentralblatt MATH:
0605.10016
[S1] Goro Shimura, Confluent hypergeometric functions on tube domains, Math. Ann. 260 (1982), no. 3, 269–302.
Mathematical Reviews (MathSciNet):
MR84f:32040
Zentralblatt MATH:
0502.10013
Digital Object Identifier: doi:10.1007/BF01461465
[S2] Goro Shimura, On Eisenstein series of half-integral weight, Duke Math. J. 52 (1985), no. 2, 281–314.
Mathematical Reviews (MathSciNet):
MR87g:11053
Zentralblatt MATH:
0577.10025
Digital Object Identifier: doi:10.1215/S0012-7094-85-05216-0
Project Euclid: euclid.dmj/1077304434
[S3] Goro Shimura, On the transformation formulas of theta series, Amer. J. Math. 115 (1993), no. 5, 1011–1052.
Mathematical Reviews (MathSciNet):
MR94h:11045
Zentralblatt MATH:
0802.11016
Digital Object Identifier: doi:10.2307/2375064
JSTOR: links.jstor.org
[S4] 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.
Mathematical Reviews (MathSciNet):
MR98h:11057
Zentralblatt MATH:
0906.11020
[S5] Goro Shimura, An exact mass formula for orthogonal groups, Duke Math. J. 97 (1999), no. 1, 1–66.
Mathematical Reviews (MathSciNet):
MR2000a:11073
Zentralblatt MATH:
01425198
Digital Object Identifier: doi:10.1215/S0012-7094-99-09701-6
Project Euclid: euclid.dmj/1077228500
[Si] C. L. Siegel, Über die analytische Theorie der quadratischen Formen, I, Ann. of Math. 36 (1935), no. 2, 527–606, II, 37(1936), 230–263; III, 38(1937), 212–291.
Zentralblatt MATH:
0012.19703
[W1] André Weil, Sur certains groupes d'opérateurs unitaires, Acta Math. 111 (1964), 143–211.
Mathematical Reviews (MathSciNet):
MR29:2324
Zentralblatt MATH:
0203.03305
Digital Object Identifier: doi:10.1007/BF02391012
[W2] André Weil, Sur la formule de Siegel dans la théorie des groupes classiques, Acta Math. 113 (1965), 1–87.
Mathematical Reviews (MathSciNet):
MR36:6421
Zentralblatt MATH:
0161.02304
Digital Object Identifier: doi:10.1007/BF02391774
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