Jacobi-sum Hecke characters of imaginary quadratic fields

Gudrun Brattström; Stephen Lichtenbaum

Compositio Mathematica (1984)

  • Volume: 53, Issue: 3, page 277-302
  • ISSN: 0010-437X

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Brattström, Gudrun, and Lichtenbaum, Stephen. "Jacobi-sum Hecke characters of imaginary quadratic fields." Compositio Mathematica 53.3 (1984): 277-302. <http://eudml.org/doc/89688>.

@article{Brattström1984,
author = {Brattström, Gudrun, Lichtenbaum, Stephen},
journal = {Compositio Mathematica},
keywords = {motives; value at zero; L-series; Jacobi-sum Hecke characters; imaginary quadratic fields; odd class number; Deligne's conjecture},
language = {eng},
number = {3},
pages = {277-302},
publisher = {Martinus Nijhoff Publishers},
title = {Jacobi-sum Hecke characters of imaginary quadratic fields},
url = {http://eudml.org/doc/89688},
volume = {53},
year = {1984},
}

TY - JOUR
AU - Brattström, Gudrun
AU - Lichtenbaum, Stephen
TI - Jacobi-sum Hecke characters of imaginary quadratic fields
JO - Compositio Mathematica
PY - 1984
PB - Martinus Nijhoff Publishers
VL - 53
IS - 3
SP - 277
EP - 302
LA - eng
KW - motives; value at zero; L-series; Jacobi-sum Hecke characters; imaginary quadratic fields; odd class number; Deligne's conjecture
UR - http://eudml.org/doc/89688
ER -

References

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  2. [B] G. Brattström: Jacobi-sum Hecke characters of a totally real abelian field, to appear in Séminaire de Théorie des Nombres, Bordeaux, exposé n° 22, 1981- 1982. Zbl0528.12011MR695338
  3. [B-S] Z.I. Borevich and I.R. Shafarevich: Number Theory, Academic Press, 1966. Zbl0145.04902MR195803
  4. [C-F] J.W.S. CASSELS and A. FROHLICH (eds.): Algebraic Number Theory, Academic Press, 1967. Zbl0153.07403MR215665
  5. [Da] R.M. Damerell: L-functions of elliptic curves with complex multiplication I. Acta Arith.17 (1970) 287-301. Zbl0209.24603MR285540
  6. [De1] P. Deligne: Valeurs de fonctions L et périodes d'intégrales. Proceedings of Symposia in Pure Mathematics 33, part 2 (1978) 313-346. Zbl0449.10022MR546622
  7. [De2] P. Deligne: Hodge cycles on abelian varieties. In: Hodge Cycles, Motives, and Shimura Varieties, Springer Lecture Notes in Mathematics900, Springer-Verlag, 1981. Zbl0537.14006
  8. [G-S] C. Goldstein and N. Schappacher: Series d'Eisenstein et fonctions L de courbes elliptiques à multiplication complexe, J. reine angew. Math.327 (1981) 184-218. Zbl0456.12007MR631315
  9. [G] B.H. Gross: Arithmetic on elliptic curves with complex multiplication. Springer Lecture Notes in Mathematics776, Springer-Verlag, 1980. Zbl0433.14032MR563921
  10. [H] E. Hecke: Mathematische Werke, Vandenhoeck und Ruprecht, 1970. Zbl0092.00102MR371577
  11. [I] K. Iwasawa: Lectures on p-adic L-functions. Ann. of Math. Studies 74Princeton Univ. Press, 1972. Zbl0236.12001MR360526
  12. [Ka] N. Katz: p-adic L-functions for CM fields. Invent. Math.49 (1978) 199-297. Zbl0417.12003MR513095
  13. [K-L] D. Kubert and S. Lichtenbaum: Jacobi-sum Hecke characters and Gauss sum identities. Comp. Math.48 (1983) 55-87. Zbl0513.12010MR700580
  14. [Ku] D. Kubert: Jacobi sums and Hecke characters (to appear). Zbl0577.12004MR784285
  15. [La1] S. Lang: Algebraic Number Theory. Addison-Wesley, 1970. Zbl0211.38404MR282947
  16. [La2] S. Lang: Elliptic Functions. Addison-Wesley, 1973. Zbl0316.14001MR409362
  17. [L] S. Lichtenbaum: Values of L-functions of Jacobi-sum Hecke characters of abelian fields. In: Number Theory Related to Fermat's Last Theorem. Birkhäuser, 1982. Zbl0518.12005MR685297
  18. [Si] W. Sinnott: On the Stickelberger ideal and the circular units of an abelian field. Invent. Math.62 (1980) 181-234. Zbl0465.12001MR595586
  19. [T] J. Tate: The arithmetic of elliptic curves. Invent. Math.23 (1974) 179-206. Zbl0296.14018MR419359
  20. [W1] A. Weil: Jacobi sums as "Grössencharaktere". Trans. Amer. Math. Soc.73 (1952) 487-495. Zbl0048.27001MR51263
  21. [W2] A. Weil: Sommes de Jacobi et caractères de Hecke. Nachrichten Akad. Wiss. Göttingen (1974) 1-14. Zbl0367.10035MR392859
  22. [W3] A. Weil: Elliptic Functions According to Eisenstein and Kronecker. Springer-Verlag (1976). Zbl0318.33004MR562289

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