Document Zbl 0513.12010

Jacobi-sum Hecke characters and Gauss-sum identities. (English) Zbl 0513.12010

Compos. Math. 48, 55-87 (1983).

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MSC:

11R42	Zeta functions and \(L\)-functions of number fields
11L10	Jacobsthal and Brewer sums; other complete character sums
11R18	Cyclotomic extensions

Keywords:

Davenport-Hasse identities; value of L-series at zero; Jacobi sums; Hecke characters; Gamma function; Gauss sums; infinity type; Weil type; Deligne type

Citations:

Zbl 0367.10035

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Full Text: Numdam EuDML

References:

[1]	A. Weil : Jacobi sums as ”Grössencharaktere” . Trans. Amer. Math. Soc. 75 (1952) 487-495. · Zbl 0048.27001 · doi:10.2307/1990804
[2]	A. Weil : Sommes de Jacobi et caractères de Hecke . Nachrich. der Akad. Göttingen (1974) 1-14. · Zbl 0367.10035
[3]	P. Deligne : Valeurs de fonctions L et périodes d’intégrales . Proceedings of Symposia in Pure Mathematics 33 (1979) 313-346. · Zbl 0449.10022
[4]	P. Deligne : Cycles de Hodge sur les varietes abeliennes , preprint.
[5]	D. Kubert : Jacobi sums and Hecke characters , to appear. · Zbl 0577.12004 · doi:10.2307/2374416
[6]	H. Davenport and H. Hasse : Die Nullstellen der Kongruenz-zeta funktionen in gewissen zyklischen Fallen . J. reine angew Math. 172 (1935) 151-182. · Zbl 0010.33803
[7]	S. Lichtenbaum : Jacobi-sum Hecke characters of imaginary quadratic fields , preprint. · Zbl 0584.12007
[8]	L. Ahlfors : Complex analysis . McGraw-Hill, 1953.
[9]	S. Lang : Algebraic number theory . Addison-Wesley, 1970. · Zbl 0211.38404
[10]	R. Langlands : unpublished manuscript.
[11]	B. Gross and N. Koblitz : Gauss sums and the p-adic \Gamma -function . Ann. of Math. 109 (1979) 569-581. · Zbl 0406.12010 · doi:10.2307/1971226
[12]	G.H. Hardy and E.M. Wright : An introduction to the theory of numbers , 4th ed. Oxford University Press, 1960. · Zbl 0086.25803
[13]	I. Iwasawa : Some remarks on Hecke characters . International Symposium on Algebraic Number Theory, Kyoto, 1976. S. Iyanaga, ed. · Zbl 0364.12010
[14]	R.J. Evans : Identities for products of Gauss sums over finite fields . To appear in L’Enseignement Math. · Zbl 0491.12020

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