The rank of quotients of $J_0 (N)$
Jeffrey M. VanderKam
Source: Duke Math. J. Volume 97, Number 3
(1999), 545-577.
First Page:
Show
Hide
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/1077228803
Mathematical Reviews number (MathSciNet): MR1682989
Zentralblatt MATH identifier: 1013.11030
Digital Object Identifier: doi:10.1215/S0012-7094-99-09721-1
References
[1] Armand Brumer, The rank of $J\sb 0(N)$, Astérisque (1995), no. 228, 3, 41–68, in Columbia University Number Theory Seminar (New York, 1992), Soc. Math. France, Montrouge.
Mathematical Reviews (MathSciNet): MR96f:11083
Zentralblatt MATH: 0851.11035
[2] D. A. Burgess, On character sums and $L$-series. II, Proc. London Math. Soc. (3) 13 (1963), 524–536.
Mathematical Reviews (MathSciNet): MR26:6133
Zentralblatt MATH: 0123.04404
Digital Object Identifier: doi:10.1112/plms/s3-13.1.524
[3] Harold Davenport, Multiplicative number theory, Graduate Texts in Mathematics, vol. 74, Springer-Verlag, New York, 1980, 2d ed.
Mathematical Reviews (MathSciNet): MR82m:10001
Zentralblatt MATH: 0453.10002
[4] W. Duke, The critical order of vanishing of automorphic $L$-functions with large level, Invent. Math. 119 (1995), no. 1, 165–174.
Mathematical Reviews (MathSciNet): MR95k:11075
Zentralblatt MATH: 0838.11035
Digital Object Identifier: doi:10.1007/BF01245178
[5] B. Gross, W. Kohnen, and D. Zagier, Heegner points and derivatives of $L$-series. II, Math. Ann. 278 (1987), no. 1-4, 497–562.
Mathematical Reviews (MathSciNet): MR89i:11069
Zentralblatt MATH: 0641.14013
Digital Object Identifier: doi:10.1007/BF01458081
[6] Benedict H. Gross and Don B. Zagier, Heegner points and derivatives of $L$-series, Invent. Math. 84 (1986), no. 2, 225–320.
Mathematical Reviews (MathSciNet): MR87j:11057
Zentralblatt MATH: 0608.14019
Digital Object Identifier: doi:10.1007/BF01388809
[7] S. Kamienny, Torsion points on elliptic curves over fields of higher degree, Internat. Math. Res. Notices (1992), no. 6, 129–133.
Mathematical Reviews (MathSciNet): MR93e:11072
Zentralblatt MATH: 0807.14022
Digital Object Identifier: doi:10.1155/S107379289200014X
[8] V. Kolyvagin and D. Logachev, Finiteness of the Shafarevich-Tate group and the group of rational points for some modular abelian varieties, Leningrad Math. J. 1 (1990), 1229–1253.
Zentralblatt MATH: 0728.14026
Mathematical Reviews (MathSciNet): MR1036843
[9] B. Mazur, Modular curves and the Eisenstein ideal, Inst. Hautes Études Sci. Publ. Math. (1977), no. 47, 33–186 (1978).
Mathematical Reviews (MathSciNet): MR80c:14015
Zentralblatt MATH: 0394.14008
Digital Object Identifier: doi:10.1007/BF02684339
[10] Loïc Merel, Bornes pour la torsion des courbes elliptiques sur les corps de nombres, Invent. Math. 124 (1996), no. 1-3, 437–449.
Mathematical Reviews (MathSciNet): MR96i:11057
Zentralblatt MATH: 0936.11037
Digital Object Identifier: doi:10.1007/s002220050059
[11] Jean-François Mestre, Formules explicites et minorations de conducteurs de variétés algébriques, Compositio Math. 58 (1986), no. 2, 209–232.
Mathematical Reviews (MathSciNet): MR87j:11059
Zentralblatt MATH: 0607.14012
[12] M. Ram Murty, The analytic rank of $J\sb 0(N)(\bf Q)$, Number theory (Halifax, NS, 1994), CMS Conf. Proc., vol. 15, Amer. Math. Soc., Providence, RI, 1995, pp. 263–277.
Mathematical Reviews (MathSciNet): MR96i:11054
Zentralblatt MATH: 0851.11036
[13] René Schoof and Marcel van der Vlugt, Hecke operators and the weight distributions of certain codes, J. Combin. Theory Ser. A 57 (1991), no. 2, 163–186.
Mathematical Reviews (MathSciNet): MR92g:94017
Zentralblatt MATH: 0729.11065
Digital Object Identifier: doi:10.1016/0097-3165(91)90016-A
[14] A. Selberg, On the zeros of Riemann's zeta-function, Skr. Norske Vid. Akad. Oslo I (1942), no. 10, reprinted in Collected Papers, Vol. I, Springer-Verlag, Berlin, 1989, 85–141.
Zentralblatt MATH: 0028.11101
Mathematical Reviews (MathSciNet): MR10712
[15] Jean-Pierre Serre, Répartition asymptotique des valeurs propres de l'opérateur de Hecke $T\sb p$, J. Amer. Math. Soc. 10 (1997), no. 1, 75–102.
Mathematical Reviews (MathSciNet): MR97h:11048
Zentralblatt MATH: 0871.11032
Digital Object Identifier: doi:10.1090/S0894-0347-97-00220-8
JSTOR: links.jstor.org
[16] Goro 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
Duke Mathematical Journal
