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EQUIVALENCES OF BIRCH AND SWINNERTON-DYER CONJECTURES OVER NON-ABELIAN EXTENSIONS OF ORDER 27
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  • Journal title : Honam Mathematical Journal
  • Volume 30, Issue 1,  2008, pp.47-51
  • Publisher : The Honam Mathematical Society
  • DOI : 10.5831/HMJ.2008.30.1.047
 Title & Authors
EQUIVALENCES OF BIRCH AND SWINNERTON-DYER CONJECTURES OVER NON-ABELIAN EXTENSIONS OF ORDER 27
Yu, Ho-Seog;
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 Abstract
By finding two characters of subgroups of the Heisenberg group whose induced characters are same, we prove that the Birch and Swinnerton-Dyer conjectures for two elliptic curves corresponding to the characters are equivalent.
 Keywords
Birch and Swinnerton-Dyer conjecture;Heisenberg group;induced character;
 Language
English
 Cited by
 References
1.
J. S. Milne, On the arithmetic of abelian varieties, Invent. Math. 11 (1972), 177-190.

2.
J. Silverman, The Arithmetic of Elliptic Curves, Grad. Texts in Math. 106. Springer-Verlag 1986.

3.
J. Tate, On the conjectures of Birch and Swinnerton-Dyer and a geometric analog, In: Seminaire Bourbaki, 1965-66, expose 306.

4.
H. Yu, Representations and factors of restriction of scalars, J. of Number Theory 109 (2004), 266-277. crossref(new window)