Duke Mathematical Journal

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

Kamal Khuri-Makdisi

Source: Duke Math. J. Volume 84, Number 2 (1996), 399-452.

First Page PDF: View first page of article (PDF, 121 KB)

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

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber.
If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text
Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.dmj/1077243836
Mathematical Reviews number (MathSciNet): MR1404335
Zentralblatt MATH identifier: 0859.11031
Digital Object Identifier: doi:10.1215/S0012-7094-96-08414-8

References

[E] A. Erdelyi, W. Magnus, F. Oberhettinger, and F. G. Tricomi, Higher Transcendental Functions, Volume 2, McGraw-Hill, New York, 1953.
Zentralblatt MATH: 0052.29502
Mathematical Reviews (MathSciNet): MR58756
[H] P Henrici, Applied and Computational Complex Analysis, Volume 2, Wiley-Interscience, New York, 1974.
Mathematical Reviews (MathSciNet): MR372162
Zentralblatt MATH: 0313.30001
[JL] H. Jacquet and R. Langlands, Automorphic forms on ${\rm GL}(2)$, Lecture Notes in Mathematics, vol. 114, Springer-Verlag, Berlin, 1970.
Mathematical Reviews (MathSciNet): MR53:5481
Zentralblatt MATH: 0236.12010
[KaSa] S. Katok and P. Sarnak, Heegner points, cycles and Maass forms, Israel J. Math. 84 (1993), no. 1-2, 193–227.
Mathematical Reviews (MathSciNet): MR94h:11051
Zentralblatt MATH: 0787.11016
[Ko] 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
[KoZa] 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
[Ma] H. Maass, Die Differentialgleichungen in der Theorie der elliptischen Modulfunktionen, Math. Ann. 125 (1953), 235–263.
Zentralblatt MATH: 0053.05601
Mathematical Reviews (MathSciNet): MR65583
Digital Object Identifier: doi:10.1007/BF01343120
[Ni] S. Niwa, Modular forms of half integral weight and the integral of certain theta-functions, Nagoya Math. J. 56 (1975), 147–161.
Mathematical Reviews (MathSciNet): MR51:361
Zentralblatt MATH: 0303.10027
[S] T. Shintani, On construction of holomorphic cusp forms of half integral weight, Nagoya Math. J. 58 (1975), 83–126.
Mathematical Reviews (MathSciNet): MR52:10603
Zentralblatt MATH: 0316.10016
[Sh1] 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
[Sh2] G. Shimura, On the periods of modular forms, Math. Ann. 229 (1977), no. 3, 211–221.
Mathematical Reviews (MathSciNet): MR57:3080
Zentralblatt MATH: 0363.10019
Digital Object Identifier: doi:10.1007/BF01391466
[Sh3] 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
[Sh4] 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
[Sh5] 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
[Sh6] 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
[Sh7] 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
[Sh8] 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
[Sh9] 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
[Sh10] G. Shimura, On the Fourier coefficients of Hilbert modular forms of half-integral weight, Duke Math. J. 71 (1993), no. 2, 501–557.
Mathematical Reviews (MathSciNet): MR94e:11046
Zentralblatt MATH: 0802.11017
Digital Object Identifier: doi:10.1215/S0012-7094-93-07121-9
Project Euclid: euclid.dmj/1077290065
[Sh11] G. 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
[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
[W] A. Weil, Dirichlet Series and Automorphic Forms, Lecture Notes in Math., vol. 189, Springer-Verlag, Berlin, 1971.
Zentralblatt MATH: 0218.10046

2010 © Duke University Press