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Duke Mathematical Journal

On the Fourier coefficients of Hilbert modular forms of half-integral weight

Goro Shimura

Source: Duke Math. J. Volume 71, Number 2 (1993), 501-557.

First Page PDF: View first page of article (PDF, 98 KB)

Primary Subjects: 11F37
Secondary Subjects: 11F30, 11F41, 11F66, 11F67

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Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.dmj/1077290065
Mathematical Reviews number (MathSciNet): MR1233447
Zentralblatt MATH identifier: 0802.11017
Digital Object Identifier: doi:10.1215/S0012-7094-93-07121-9

References

[H]1 E. Hecke, Über Modulfunktionen und die Dirichletschen Reihen mit Eulerscher Produktentwicklung I, Math. Ann. 114 (1937), 1–28.
Zentralblatt MATH: 0015.40202
Mathematical Reviews (MathSciNet): MR1513122
Digital Object Identifier: doi:10.1007/BF01594160
[H]2 E. Hecke, Über Modulfunktionen und die Dirichletschen Reihen mit Eulerscher Produktentwicklung II, Math. Ann. 114 (1937), 316–351.
Zentralblatt MATH: 0016.35503
Mathematical Reviews (MathSciNet): MR1513142
Digital Object Identifier: doi:10.1007/BF01594180
[H]3 E. Hecke, Mathematische Werke, Herausgegeben im Auftrage der Akademie der Wissenschaften zu Göttingen, Vandenhoeck & Ruprecht, Göttingen, 1959, # # 35 and 36.
Mathematical Reviews (MathSciNet): MR21:3303
Zentralblatt MATH: 0092.00102
[K] W. Kohnen, Fourier coefficients of modular forms of half-integral weight, Math. Ann. 271 (1985), no. 2, 237–268.
Mathematical Reviews (MathSciNet): MR86i:11018
Zentralblatt MATH: 0542.10018
Digital Object Identifier: doi:10.1007/BF01455989
[KZ] W. Kohnen and D. Zagier, Values of $L$-series of modular forms at the center of the critical strip, Invent. Math. 64 (1981), no. 2, 175–198.
Mathematical Reviews (MathSciNet): MR83b:10029
Zentralblatt MATH: 0468.10015
Digital Object Identifier: doi:10.1007/BF01389166
[N] S. Niwa, On Fourier coefficients and certain “periods” of modular forms, Proc. Japan Acad. Ser. A Math. Sci. 58 (1982), no. 2, 90–92.
Mathematical Reviews (MathSciNet): MR83h:10062
Zentralblatt MATH: 0524.10018
[73] G. Shimura, On modular forms of half integral weight, Ann. of Math. (2) 97 (1973), 440–481.
Mathematical Reviews (MathSciNet): MR48:10989
Zentralblatt MATH: 0266.10022
Digital Object Identifier: doi:10.2307/1970831
JSTOR: links.jstor.org
[75] G. Shimura, On the holomorphy of certain Dirichlet series, Proc. London Math. Soc. (3) 31 (1975), no. 1, 79–98.
Mathematical Reviews (MathSciNet): MR52:3064
Zentralblatt MATH: 0311.10029
[76] G. Shimura, The special values of the zeta functions associated with cusp forms, Comm. Pure Appl. Math. 29 (1976), no. 6, 783–804.
Mathematical Reviews (MathSciNet): MR55:7925
Zentralblatt MATH: 0348.10015
[78]1 G. Shimura, The special values of the zeta functions associated with Hilbert modular forms, Duke Math. J. 45 (1978), no. 3, 637–679.
Mathematical Reviews (MathSciNet): MR80a:10043
Zentralblatt MATH: 0394.10015
Digital Object Identifier: doi:10.1215/S0012-7094-78-04529-5
Project Euclid: euclid.dmj/1077312955
[78]2 G. Shimura, Corrections to: “The special values of the zeta functions associated with Hilbert modular forms”, Duke Math. J. 48 (1981), no. 3, 697.
Mathematical Reviews (MathSciNet): MR82j:10051
Zentralblatt MATH: 0464.10016
Digital Object Identifier: doi:10.1215/S0012-7094-81-04838-9
Project Euclid: euclid.dmj/1077314788
[80] G. Shimura, The arithmetic of certain zeta functions and automorphic forms on orthogonal groups, Ann. of Math. (2) 111 (1980), no. 2, 313–375.
Mathematical Reviews (MathSciNet): MR81g:10041
Zentralblatt MATH: 0438.12003
Digital Object Identifier: doi:10.2307/1971202
JSTOR: links.jstor.org
[81] G. Shimura, The critical values of certain zeta functions associated with modular forms of half-integral weight, J. Math. Soc. Japan 33 (1981), no. 4, 649–672.
Mathematical Reviews (MathSciNet): MR83b:10030
Zentralblatt MATH: 0494.10018
[82]1 G. Shimura, The periods of certain automorphic forms of arithmetic type, J. Fac. Sci. Univ. Tokyo Sect. IA Math. 28 (1981), no. 3, 605–632 (1982).
Mathematical Reviews (MathSciNet): MR84f:10040
Zentralblatt MATH: 0499.10027
[82]2 G. 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
[83] G. Shimura, On Eisenstein series, Duke Math. J. 50 (1983), no. 2, 417–476.
Mathematical Reviews (MathSciNet): MR84k:10019
Zentralblatt MATH: 0519.10019
Digital Object Identifier: doi:10.1215/S0012-7094-83-05019-6
Project Euclid: euclid.dmj/1077303203
[85]1 G. 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
[85]2 G. Shimura, On the Eisenstein series of Hilbert modular groups, Rev. Mat. Iberoamericana 1 (1985), no. 3, 1–42.
Mathematical Reviews (MathSciNet): MR87h:11038
Zentralblatt MATH: 0608.10028
[87] G. Shimura, On Hilbert modular forms of half-integral weight, Duke Math. J. 55 (1987), no. 4, 765–838.
Mathematical Reviews (MathSciNet): MR89a:11054
Zentralblatt MATH: 0636.10024
Digital Object Identifier: doi:10.1215/S0012-7094-87-05538-4
Project Euclid: euclid.dmj/1077306298
[88] G. Shimura, On the critical values of certain Dirichlet series and the periods of automorphic forms, Invent. Math. 94 (1988), no. 2, 245–305.
Mathematical Reviews (MathSciNet): MR90e:11069
Zentralblatt MATH: 0656.10018
Digital Object Identifier: doi:10.1007/BF01394326
[90] G. Shimura, On the fundamental periods of automorphic forms of arithmetic type, Invent. Math. 102 (1990), no. 2, 399–428.
Mathematical Reviews (MathSciNet): MR91k:11041
Zentralblatt MATH: 0712.11028
Digital Object Identifier: doi:10.1007/BF01233433
[91] G. Shimura, The critical values of certain Dirichlet series attached to Hilbert modular forms, Duke Math. J. 63 (1991), no. 3, 557–613.
Mathematical Reviews (MathSciNet): MR92e:11045
Zentralblatt MATH: 0752.11021
Digital Object Identifier: doi:10.1215/S0012-7094-91-06324-6
Project Euclid: euclid.dmj/1077296070
[Wa] J.-L. Waldspurger, Sur les coefficients de Fourier des formes modulaires de poids demi-entier, J. Math. Pures Appl. (9) 60 (1981), no. 4, 375–484.
Mathematical Reviews (MathSciNet): MR83h:10061
Zentralblatt MATH: 0431.10015
[We] A. 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

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