Miki, Hiroo
On the conductor of the Jacobi sum Hecke character
Compositio Mathematica, Tome 92 (1994) no. 1 , p. 23-41
Zbl 0798.11049 | MR 1275719
URL stable : http://www.numdam.org/item?id=CM_1994__92_1_23_0

Bibliographie

1 Anderson, G.: The hyperadelic gamma function, Invent. Math. 95 (1989) 63-131. MR 969414 | Zbl 0682.14011

2 Artin, Ed., Hasse, H.: Die beiden Ergänzungssätze zum Reziprozitätsgesetz der ln-ten Potenzreste im Körper der ln-ten Einheitswureln, Abh. Math. Sem. Univ. Hamburg 6 (1928) 146-162. JFM 54.0191.05

3 Coates, J., Wiles, A.: Explicit reciprocity laws, Astérisque 41/42 (1977) 7-17. MR 460333 | Zbl 0358.12001

4 Coleman, R.: Anderson-Ihara theory: Gauss sums and circular units, Advanced Studies in Pure Math. 17 (1989) 55-72. MR 1097609 | Zbl 0733.14012

5 Coleman, R., Mccallum, W.: Stable reduction of Fermat curves and Jacobi sum Hecke characters, J. reine und angew. Math. 385 (1988) 41-101. MR 931215 | Zbl 0654.12003

6 Hasse, H.: Zetafunktionen und L-Funktionen zu einem arithmetischen Funktionenkörper vom Fermatschen Typus. Abh. Deut. Akad. Wiss. Berlin Kl. Math. Nat., 1954, no. 4 (1955) 70 pp. MR 76807 | Zbl 0068.03501

7 Ihara, Y.: Profinite braid groups, Galois representations and complex multiplications, Ann. of Math. 123 (1986), 43-106. MR 825839 | Zbl 0595.12003

8 Iwasawa, K.: On explicit formulas for the norm residue symbol, J. Math. Soc. Japan 20 (1968) 151-165. MR 229609 | Zbl 0256.12013

9 Iwasawa, K.: On p-adic L-functions, Ann. of Math. 89 (1969) 198-205. MR 269627 | Zbl 0186.09201

10 Iwasawa, K.: Lectures on p-adic L-functions. Ann. of Math. Studies 74, Princeton University Press 1972. MR 360526 | Zbl 0236.12001

11 Iwasawa, K.: A note on Jacobi sums, Symposia Math. 15 (1975) 447-459. MR 384747 | Zbl 0324.12007

12 Jensen, C.: Über die Führer einer Klasse Heckescher Grössencharaktere, Math. Scand. 8 (1960) 81-96. MR 125109 | Zbl 0204.07004

13 Kato, K.: A generalization of class field theory (Japanese). Sûgaku 40 (1988) 289-311. MR 1002305 | Zbl 0717.11050

14 Miki, H.: On the l-adic expansion of certain Gauss sums and its applications, Advanced Studies in Pure Math. 12 (1987) 87-118. MR 948238 | Zbl 0649.12002

15 Miki, H.: On Weil's Grössencharacters: A brief survey of Gauss and Jacobi sums and recent developments. Proc. Symp. on Number Theory, Nagasaki, Japan, Nov. 1986.

16 Miki, H.: On the conductor of the Jacobi sum Hecke character. Preprint April 1988, 10 pp. (unpublished) = talk in Number Theory Seminar (Goldfeld), Columbia Univ., March 21, 1988.

17 Miki, H.: On the congruence for Gauss sums and its applications. In: Théorie des nombres- Number Theory, J.-M. De Koninck, C. Levesque (eds.). Proceedings, Laval 1987, pp. 632-641. Walter de Gruyter: Berlin, New York, 1989. MR 1024592 | Zbl 0715.11041

18 Miki, H.: On the calculation of certain Hilbert norm residue symbols and its application. Preprint March 1992 = the details of a part of [16]. MR 1310737 | Zbl 0829.11053

19 Rohrlich, D.: Jacobi sums and explcit reciprocity laws. Compositio Math. 60 (1986) 97-114. Numdam | MR 867959 | Zbl 0612.12007

20 Schmidt, C.- G.: Über die Führer von Gaußschen Summen als Größencharaktere, J. Number Theory 12 (1980) 283-310. MR 586458 | Zbl 0446.12002

21 Shimura, G., Taniyama, Y.: Complex Multiplication of Abelian Varieties and its Applications to Number Theory, Publ. of Math. Soc. Japan, 1961. MR 125113 | Zbl 0112.03502

22 Washington, L.: Introduction to Cyclotomic Fields. GTM 83 (Springer: Berlin, Heidelberg, New York), 1982. MR 718674 | Zbl 0484.12001

23 Weil, A.: Jacobi sums as "Grössencharaktere" Trans. Amer. Math. Soc. 73 (1952) 487-495. MR 51263 | Zbl 0048.27001