Jacobi-sum Hecke characters and Gauss-sum identities

Daniel S. Kubert; Stephen Lichtenbaum

Compositio Mathematica (1983)

  • Volume: 48, Issue: 1, page 55-87
  • ISSN: 0010-437X

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Kubert, Daniel S., and Lichtenbaum, Stephen. "Jacobi-sum Hecke characters and Gauss-sum identities." Compositio Mathematica 48.1 (1983): 55-87. <http://eudml.org/doc/89587>.

@article{Kubert1983,
author = {Kubert, Daniel S., Lichtenbaum, Stephen},
journal = {Compositio Mathematica},
keywords = {Davenport-Hasse identities; value of L-series at zero; Jacobi sums; Hecke characters; Gamma function; Gauss sums; infinity type; Weil type; Deligne type},
language = {eng},
number = {1},
pages = {55-87},
publisher = {Martinus Nijhoff Publishers},
title = {Jacobi-sum Hecke characters and Gauss-sum identities},
url = {http://eudml.org/doc/89587},
volume = {48},
year = {1983},
}

TY - JOUR
AU - Kubert, Daniel S.
AU - Lichtenbaum, Stephen
TI - Jacobi-sum Hecke characters and Gauss-sum identities
JO - Compositio Mathematica
PY - 1983
PB - Martinus Nijhoff Publishers
VL - 48
IS - 1
SP - 55
EP - 87
LA - eng
KW - Davenport-Hasse identities; value of L-series at zero; Jacobi sums; Hecke characters; Gamma function; Gauss sums; infinity type; Weil type; Deligne type
UR - http://eudml.org/doc/89587
ER -

References

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  1. [1] A. Weil: Jacobi sums as "Grössencharaktere". Trans. Amer. Math. Soc.75 (1952) 487-495. Zbl0048.27001MR51263
  2. [2] A. Weil: Sommes de Jacobi et caractères de Hecke. Nachrich. der Akad. Göttingen (1974) 1-14. Zbl0367.10035MR392859
  3. [3] P. Deligne: Valeurs de fonctions L et périodes d'intégrales. Proceedings of Symposia in Pure Mathematics 33 (1979) 313-346. Zbl0449.10022MR546622
  4. [4] P. Deligne: Cycles de Hodge sur les varietes abeliennes, preprint. 
  5. [5] D. Kubert: Jacobi sums and Hecke characters, to appear. Zbl0577.12004MR784285
  6. [6] H. Davenport and H. Hasse: Die Nullstellen der Kongruenz-zeta funktionen in gewissen zyklischen Fallen. J. reine angew Math.172 (1935) 151-182. Zbl0010.33803JFM60.0913.01
  7. [7] S. Lichtenbaum: Jacobi-sum Hecke characters of imaginary quadratic fields, preprint. Zbl0584.12007
  8. [8] L. Ahlfors: Complex analysis. McGraw-Hill, 1953. MR510197
  9. [9] S. Lang: Algebraic number theory. Addison-Wesley, 1970. Zbl0211.38404MR282947
  10. [10] R. Langlands : unpublished manuscript. 
  11. [11] B. Gross and N. Koblitz: Gauss sums and the p-adic Γ-function. Ann. of Math.109 (1979) 569-581. Zbl0406.12010
  12. [12] G.H. Hardy and E.M. Wright: An introduction to the theory of numbers, 4th ed. Oxford University Press, 1960. Zbl0086.25803MR67125
  13. [13] I. Iwasawa: Some remarks on Hecke characters. International Symposium on Algebraic Number Theory, Kyoto, 1976. S. Iyanaga, ed. Zbl0364.12010
  14. [14] R.J. Evans: Identities for products of Gauss sums over finite fields. To appear in L'Enseignement Math. Zbl0491.12020MR659148

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