The non-vanishing of certain Hecke $L$-functions at the center of the critical strip
David E. Rohrlich
Source: Duke Math. J. Volume 47, Number 1
(1980), 223-232.
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Permanent link to this document: http://projecteuclid.org/euclid.dmj/1077313872
Mathematical Reviews number (MathSciNet): MR563377
Zentralblatt MATH identifier: 0434.12007
Digital Object Identifier: doi:10.1215/S0012-7094-80-04716-X
References
[1] N. Arthaud, On Birch and Swinnerton-Dyer's conjecture for elliptic curves with complex multiplication II, to appear.
[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] A. Selberg and S. Chowla, On Epstein's zeta-function, J. Reine Angew. Math. 227 (1967), 86–110.
Mathematical Reviews (MathSciNet): MR35:6632
Zentralblatt MATH: 0166.05204
Digital Object Identifier: doi:10.1515/crll.1967.227.86
[4] J. Coates and A. Wiles, On the conjecture of Birch and Swinnerton-Dyer, Invent. Math. 39 (1977), no. 3, 223–251.
Mathematical Reviews (MathSciNet): MR57:3134
Zentralblatt MATH: 0359.14009
Digital Object Identifier: doi:10.1007/BF01402975
[5] M. Deuring, Imaginäre quadratische Zahlkörper mit der Klassenzahl I, Math. Z. 37 (1933), 403–413.
Zentralblatt MATH: 0007.29602
[6] B. Gross, Arithmetic on elliptic curves with complex multiplication, to appear in Springer Lecture Notes.
Mathematical Reviews (MathSciNet): MR563921
[7] D. R. Heath-Brown, Hybrid bounds for Dirichlet $L$-functions, Invent. Math. 47 (1978), no. 2, 149–170.
Mathematical Reviews (MathSciNet): MR58:5549
Zentralblatt MATH: 0362.10035
Digital Object Identifier: doi:10.1007/BF01578069
[8] E. Hecke, Mathematische Werke, Herausgegeben im Auftrage der Akademie der Wissenschaften zu Göttingen, Vandenhoeck & Ruprecht, Göttingen, 1959.
Mathematical Reviews (MathSciNet): MR21:3303
Zentralblatt MATH: 0092.00102
[9] S. Lang, Introduction to modular forms, Springer-Verlag, Berlin, 1976.
Mathematical Reviews (MathSciNet): MR55:2751
Zentralblatt MATH: 0344.10011
[10] D. Rohrlich, Galois conjugacy of unramified twists of Hecke characters, to appear.
Mathematical Reviews (MathSciNet): MR587174
Zentralblatt MATH: 0446.12011
Digital Object Identifier: doi:10.1215/S0012-7094-80-04742-0
Project Euclid: euclid.dmj/1077314189
[11] G. Shimura, The special values of the zeta functions associated with cusp forms, Comm. Pure Appl. Math. 29 (1976), no. 6, 783–804.
Mathematical Reviews (MathSciNet): MR55:7925
Zentralblatt MATH: 0348.10015
Digital Object Identifier: doi:10.1002/cpa.3160290618
[12] 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
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