Duke Mathematical Journal

The special values of the zeta functions associated with Hilbert modular forms

Goro Shimura
Source: Duke Math. J. Volume 45, Number 3 (1978), 637-679.
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Primary Subjects: 10D20
Secondary Subjects: 10H10
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Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.dmj/1077312955
Mathematical Reviews number (MathSciNet): MR507462
Zentralblatt MATH identifier: 0394.10015
Digital Object Identifier: doi:10.1215/S0012-7094-78-04529-5

References

[1] P. Garrett, Arithmetic automorphic forms for quaternion unitary groups, Thesis, Princeton University, 1977.
[2] H. Jacquet, Automorphic forms on $\rm GL(2)$. Part II, Lecture Notes in Mathematics, vol. 278, Springer-Verlag, Berlin, 1972.
Mathematical Reviews (MathSciNet): MR58:27778
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[3] H. Jacquet and R. P. Langlands, Automorphic forms on $\rm GL(2)$, Lecture Notes in Mathematics, vol. 114, Springer-Verlag, Berlin, 1970.
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[4] H. Klingen, Über den arithmetischen Charakter der Fourierkoeffizienten von Modulformen, Math. Ann. 147 (1962), 176–188.
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[5] H. D. Kloosterman, Theorie der Eisensteinschen Reihen von mehreren Veränderlichen, Abh. Math. Sem. Hamb. 6 (1928), 163–188.
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Digital Object Identifier: doi:10.2307/1970534
[7] T. Miyake, On automorphic forms on $\rm GL\sb2$ and Hecke operators, Ann. of Math. (2) 94 (1971), 174–189.
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[8] G. Shimura, On Dirichlet series and abelian varieties attached to automorphic forms, Ann. of Math. (2) 76 (1962), 237–294.
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[9] G. Shimura, On canonical models of arithmetic quotients of bounded symmetric domains, Ann. of Math. (2) 91 (1970), 144–222.
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[10] G. Shimura, Introduction to the arithmetic theory of automorphic functions, Publications of the Mathematical Society of Japan, No. 11. Iwanami Shoten, Publishers, Tokyo, 1971.
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[11] G. Shimura, On modular forms of half integral weight, Ann. of Math. (2) 97 (1973), 440–481.
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[12] G. Shimura, On some arithmetic properties of modular forms of one and several variables, Ann. of Math. (2) 102 (1975), no. 3, 491–515.
Mathematical Reviews (MathSciNet): MR58:10758
Zentralblatt MATH: 0327.10028
Digital Object Identifier: doi:10.2307/1971041
[13] G. Shimura, On the Fourier coefficients of modular forms of several variables, Nachr. Akad. Wiss. Göttingen Math.-Phys. Kl. II (1975), no. 17, 261–268.
Mathematical Reviews (MathSciNet): MR58:5528
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[14] G. Shimura, Theta functions with complex multiplication, Duke Math. J. 43 (1976), no. 4, 673–696.
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Digital Object Identifier: doi:10.1215/S0012-7094-76-04353-2
Project Euclid: euclid.dmj/1077311943
[15] G. Shimura, The special values of the zeta functions associated with cusp forms, Comm. Pure Appl. Math. 29 (1976), no. 6, 783–804.
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[16] G. Shimura, On the derivatives of theta functions and modular forms, Duke Math. J. 44 (1977), no. 2, 365–387.
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Zentralblatt MATH: 0371.14023
Digital Object Identifier: doi:10.1215/S0012-7094-77-04416-7
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[17] G. Shimura, On the periods of modular forms, Math. Ann. 229 (1977), no. 3, 211–221.
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Zentralblatt MATH: 0363.10019
Digital Object Identifier: doi:10.1007/BF01391466
[18] G. Shimura, On certain reciprocity-laws for theta functions and modular forms, Acta Math. 141 (1978), no. 1-2, 35–71.
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[19] C. L. Siegel, The volume of the fundamental domain for some infinite groups, Trans. Amer. Math. Soc. 39 (1936), no. 2, 209–218.
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[20] J. Sturm, Thesis, Princeton University, to be published, 1977.
[21] A. Weil, Dirichlet series and automorphic forms, Lecture Notes in Mathematics, vol. 189, Springer, 1970.
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[22] D. Zagier, Modular forms whose Fourier coefficients involve zeta-functions of quadratic fields, Modular functions of one variable, VI (Proc. Second Internat. Conf., Univ. Bonn, Bonn, 1976), Springer, Berlin, 1977, 105–169. Lecture Notes in Math., Vol. 627.
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Zentralblatt MATH: 0372.10017

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