$E(K/k)$ and other arithmetical invariants for finite Galois extensions

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$E(K/k)$ and other arithmetical invariants for finite Galois extensions

Shin-ichi Katayama

Source: Nagoya Math. J. Volume 114 (1989), 135-142.

First Page: Show

Primary Subjects: 11R29

Secondary Subjects: 11R32

Full-text: Open access

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Permanent link to this document: http://projecteuclid.org/euclid.nmj/1118781270
Mathematical Reviews number (MathSciNet): MR1001492
Zentralblatt MATH identifier: 0671.12002

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References

[1] J. Casseles and A. Frhlich, Algebraic Number Theory, Acad. Press, New York, 1967.

[2] Y. Furuta, The genus field and genus number in algebraic number fields, Nagoya Math. J., 29 (1967), 281-285.

Mathematical Reviews (MathSciNet): MR35:162

Zentralblatt MATH: 0166.05901

Project Euclid: euclid.nmj/1118802021

[3] S. Katayama, Class number relations of algebraic tori I, Proc. Japan Acad., 62 (1986), 216-218.

Mathematical Reviews (MathSciNet): MR87m:11035

Zentralblatt MATH: 0613.12004

Digital Object Identifier: doi:10.3792/pjaa.62.216

Project Euclid: euclid.pja/1195514262

[4] The Euler number and other arithmetical invariants for finite Galois ex- tensions of algebraic number fields, ibid., 63A (1987), 27-30.

Mathematical Reviews (MathSciNet): MR88m:11095

Zentralblatt MATH: 0623.12008

Digital Object Identifier: doi:10.3792/pjaa.63.27

Project Euclid: euclid.pja/1195513986

[5] T. Ono, Arithmetic of algebraic tori, Ann. of Math., 74 (1961), 101-139.

Mathematical Reviews (MathSciNet): MR23:A1640

Zentralblatt MATH: 0119.27801

Digital Object Identifier: doi:10.2307/1970307

[6] T. Ono, On the Tamagawa number of algebraic tori, ibid., 78 (1963), 47-73.

Mathematical Reviews (MathSciNet): MR28:94

Zentralblatt MATH: 0122.39101

Digital Object Identifier: doi:10.2307/1970502

[7] T. Ono, On some class number relations for Galois extensions Nagoya Math. J., 107 (1987), 121-133.

Mathematical Reviews (MathSciNet): MR89f:11153

Zentralblatt MATH: 0642.12018

Project Euclid: euclid.nmj/1118780772

[8] T. Ono, Algebraic groups and number theory, Sgaku, 38 (1986), 218-231 (in Japanese).

Mathematical Reviews (MathSciNet): MR88f:11030

[9] R. Sasaki, Some remarks to Ono's theorem on the generalization of Gauss's genus theory (preprint).

Mathematical Reviews (MathSciNet): MR90d:11123

Zentralblatt MATH: 0629.12007

Project Euclid: euclid.nmj/1118781056

[10] A. Weil, Adeles and Algebraic Groups,notes by M. Demazure and T. Ono, Progress in Math., 23, Birkhauser, 1982.

Mathematical Reviews (MathSciNet): MR83m:10032

Zentralblatt MATH: 0493.14028

[11] H. Yokoi, On some class number of relatively cyclic number fields, Nagoya Math. J., 29 (1967), 31-44. Department of Mathematics Collegeof General Education Tokushima University Tokushima, 770 Japan

Mathematical Reviews (MathSciNet): MR34:7496

Zentralblatt MATH: 0166.05803

Project Euclid: euclid.nmj/1118801994

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