Duke Mathematical Journal

Explicit elliptic units, I

Farshid Hajir and Fernando Rodriguez Villegas
Source: Duke Math. J. Volume 90, Number 3 (1997), 495-521.
First Page: Show Hide
Primary Subjects: 11G16
Secondary Subjects: 11R27
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/1077232812
Mathematical Reviews number (MathSciNet): MR1480544
Zentralblatt MATH identifier: 0898.11025
Digital Object Identifier: doi:10.1215/S0012-7094-97-09013-X

References

[Ab] N. H. Abel, Recherches sur les fonctions elliptiques, J. Reine Angew Math. 2 (1828), 160–190, reprinted in Oeuvres completes de Niels Henrik Abel, Vol. 1, Gröndahl, Oslo, 1881, 380–382.
[AM] A. O. L. Atkin and F. Morain, Elliptic curves and primality proving, Math. Comp. 61 (1993), no. 203, 29–68.
Mathematical Reviews (MathSciNet): MR93m:11136
Zentralblatt MATH: 0792.11056
Digital Object Identifier: doi:10.2307/2152935
[De] M. Deuring, Die Klassenkörper der komplexen Multiplikation, Enzyklopädie der mathematischen Wissenschaften: Mit Einschluss ihrer Anwendungen, Band I 2, Heft 10, Teil II (Article I 2, vol. 23, B. G. Teubner Verlagsgesellschaft, Stuttgart, 1958.
Mathematical Reviews (MathSciNet): MR29:4754
Zentralblatt MATH: 0123.04001
[Gr] B. H. Gross, Minimal models for elliptic curves with complex multiplication, Compositio Math. 45 (1982), no. 2, 155–164.
Mathematical Reviews (MathSciNet): MR84j:14044
Zentralblatt MATH: 0541.14010
[GZ] B. H. Gross and D. Zagier, On singular moduli, J. Reine Angew. Math. 355 (1985), 191–220.
Mathematical Reviews (MathSciNet): MR86j:11041
Zentralblatt MATH: 0545.10015
[H1] F. Hajir, Elliptic units of cyclic unramified extensions of complex quadratic fields, Acta Arith. 64 (1993), no. 1, 69–85.
Mathematical Reviews (MathSciNet): MR94h:11102
Zentralblatt MATH: 0787.11023
[H2] F. Hajir, Unramified elliptic units, thesis, Massachusetts Inst. of Technology, 1993.
[He] G. Herglotz, Über das quadratische Reziprozitätsgesetz in imaginären quadratischen Zahlkörpern, Leipziger Ber. 73 (1921), 303–310, Gesammelte Schriften, §20, Vandenhoeck and Ruprecht, Göttingen, 1979.
Zentralblatt MATH: 48.0170.02
[Hu] A. Hurwitz, Grundlagen einer independenten Theorie der elliptischen Modulfunctionen und Theorie der Multiplikator-Gleichungen erster Stufe, Math. Ann. 18 (1881), 528–592.
Zentralblatt MATH: 13.0364.01
[Kr] L. Kronecker, Zur Theorie der Elliptischen Funktionen, Leopold Kronecker's Werke, Vol. 4, Teubner, Leipzig, 1929, Vol. 5, 1–132, pp. 347–495.
[KL] D. S. Kubert and S. Lang, Modular units, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Science], vol. 244, Springer-Verlag, New York, 1981.
Mathematical Reviews (MathSciNet): MR84h:12009
Zentralblatt MATH: 0492.12002
[Ro] G. Robert, Unités elliptiques, Société Mathématique de France, Paris, 1973.
Mathematical Reviews (MathSciNet): MR57:9669
Zentralblatt MATH: 0314.12006
[Sc] R. Schertz, Zur Theorie der Ringklassenkörper über imaginär-quadratischen Zahlkörpern, J. Number Theory 10 (1978), no. 1, 70–82.
Mathematical Reviews (MathSciNet): MR58:594
Zentralblatt MATH: 0372.12013
Digital Object Identifier: doi:10.1016/0022-314X(78)90009-4
[Sh] G. Shimura, Introduction to the arithmetic theory of automorphic functions, Publications of the Mathematical Society of Japan, No. 11. Iwanami Shoten, Publishers, Tokyo, 1971.
Mathematical Reviews (MathSciNet): MR47:3318
Zentralblatt MATH: 0221.10029
[Si] C. L. Siegel, Advanced analytic number theory, Tata Institute of Fundamental Research Studies in Mathematics, vol. 9, Tata Institute of Fundamental Research, Bombay, 1980.
Mathematical Reviews (MathSciNet): MR83m:10001
Zentralblatt MATH: 0478.10001
[St] H. M. Stark, $L$-functions at $s=1$. IV. First derivatives at $s=0$, Adv. in Math. 35 (1980), no. 3, 197–235.
Mathematical Reviews (MathSciNet): MR81f:10054
Zentralblatt MATH: 0475.12018
Digital Object Identifier: doi:10.1016/0001-8708(80)90049-3
[Wa] G. N. Watson, Singular Moduli, III, Proc. London Math. Soc. (3) 40 (1936), 83–142.
Zentralblatt MATH: 0012.19702
[We] H. Weber, Lehrbuch der Algebra, Vol. 3, Chelsea, New York, 1961.

2012 © Duke University Press

Duke Mathematical Journal

Duke Mathematical Journal

Turn MathJax Off
What is MathJax?