Galois theory, elliptic curves, and root numbers

David E. Rohrlich

Compositio Mathematica (1996)

  • Volume: 100, Issue: 3, page 311-349
  • ISSN: 0010-437X

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Rohrlich, David E.. "Galois theory, elliptic curves, and root numbers." Compositio Mathematica 100.3 (1996): 311-349. <http://eudml.org/doc/90432>.

@article{Rohrlich1996,
author = {Rohrlich, David E.},
journal = {Compositio Mathematica},
keywords = {Birch-Swinnerton-Dyer conjecture; Deligne-Gross conjecture; -function; elliptic curve; root number; local representations},
language = {eng},
number = {3},
pages = {311-349},
publisher = {Kluwer Academic Publishers},
title = {Galois theory, elliptic curves, and root numbers},
url = {http://eudml.org/doc/90432},
volume = {100},
year = {1996},
}

TY - JOUR
AU - Rohrlich, David E.
TI - Galois theory, elliptic curves, and root numbers
JO - Compositio Mathematica
PY - 1996
PB - Kluwer Academic Publishers
VL - 100
IS - 3
SP - 311
EP - 349
LA - eng
KW - Birch-Swinnerton-Dyer conjecture; Deligne-Gross conjecture; -function; elliptic curve; root number; local representations
UR - http://eudml.org/doc/90432
ER -

References

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  1. 1 Buhler, J.: Icosahedral Galois Representations, Lect. Notes in Math.654, Springer-Verlag, 1978. Zbl0374.12002MR506171
  2. 2 Deligne, P.: Les constantes des équations fonctionelles des fonctions L, Modular Functions of One Variable, II, Lect. Notes in Math. 349, Springer-Verlag, 1973, pp. 501-595. Zbl0271.14011MR349635
  3. 3 Deligne, P.: Les constantes locales de l'équation fonctionelle de la fonction L d'Artin d'une représentation orthogonale, Invent. Math.35 (1976) 299-316. Zbl0337.12012MR506172
  4. 4 Fröhlich, A. and Queyrut, J.: On the functional equation for the Artin L-function for characters of real representations, Invent. Math.20 (1973) 125-138. Zbl0256.12010MR321888
  5. 5 Greenberg, R.: Non-vanishing of certain values of L-functions, Analytic Number Theory and Diophantine Problems, Prog. in Math.70, Birkhauser, Boston, 1987, pp. 223-235. Zbl0629.12010MR1018378
  6. 6 Kramer, K. and Tunnell, J.: Elliptic curves and local ε-factors, Compos. Math.46 (1982) 307-352. Zbl0496.14030
  7. 7 LaMacchia, S.E.: Polynomials with Galois group PSL(2, 7), Comm. in Algebra8 (1980) 983-992. Zbl0436.12005MR573466
  8. 8 Manduchi, E.: Root numbers of fibers of elliptic surfaces, Compos. Math. (to appear). Zbl0878.14028MR1352567
  9. 9 Matzat, B.H.: Konstruktive Galoistheorie, Lect. Notes in Math. 1284, Springer-Verlag, 1987. Zbl0634.12011MR1004467
  10. 10 Rohrlich, D.E.: The vanishing of certain Rankin-Selberg convolutions, Automorphic Forms and Analytic Number Theory, Les publications CRM, Montreal, 1990, pp. 123-133. Zbl0737.11014MR1111015
  11. 11 Rohrlich, D.E.: Variation of the root number on families of elliptic curves, Compos. Math.87 (1993) 119-151. Zbl0791.11026MR1219633
  12. 12 Rohrlich, D.E.: Elliptic curves and the Weil-Deligne group, Elliptic Curves and Related Topics, CRM Proceedings & Lecture Notes Vol. 4, Amer Math. Soc., Providence, 1994, pp. 125-157. Zbl0852.14008MR1260960
  13. 13 Serre, J-P.: Conducteurs d'Artin des caractères réels, Invent. Math.14 (1971) 173-183. Zbl0229.13006MR321908
  14. 14 Serre, J-P.Propriétés galoisiennes des points d'ordre fini des courbes elliptiques, Invent. Math.15 (1972), 259-331. Zbl0235.14012MR387283
  15. 15 Serre, J-P.: Local Fields, GTM vol 67, Springer-Verlag, 1979. Zbl0423.12016MR554237
  16. 16 Serre, J-P. and Tate, J.: Good reduction of abelian varieties, Ann. Math.88 (1968) 492-517. Zbl0172.46101MR236190
  17. 17 Silverman, J.H.: The Arithmetic of Elliptic Curves, GTM106, Springer-Verlag, 1985. Zbl0585.14026MR817210
  18. 18 Tate, J.: Number theoretic background, Automorphic Forms, Representations, and L -Functions, Proc. Symp. Pure Math. Vol. 33 - Part 2, Amer. Math. Soc., Providence, 1979. Zbl0422.12007MR546607
  19. 19 Weil, A.: Adeles and Algebraic Groups, Notes by M. Demazure and T. Ono, Birkhauser-Boston, Boston, 1982. Zbl0493.14028MR670072

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