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.
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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
[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
Digital Object Identifier: doi:10.1007/BF02761700
[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
Project Euclid: euclid.nmj/1118795278
[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
Project Euclid: euclid.nmj/1118795445
[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
JSTOR: links.jstor.org
[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
Digital Object Identifier: doi:10.2307/2375064
JSTOR: links.jstor.org
[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
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