Proceedings of the Japan Academy, Series A, Mathematical Sciences

On a problem of R. Brauer on zeta-functions of algebraic number fields

Ken-ichi Sato

Full-text: Open access

Article information

Source
Proc. Japan Acad. Ser. A Math. Sci., Volume 61, Number 10 (1985), 305-307.

Dates
First available in Project Euclid: 19 November 2007

Permanent link to this document
https://projecteuclid.org/euclid.pja/1195514530

Digital Object Identifier
doi:10.3792/pjaa.61.305

Mathematical Reviews number (MathSciNet)
MR834533

Zentralblatt MATH identifier
0588.12007

Subjects
Primary: 11R42: Zeta functions and $L$-functions of number fields [See also 11M41, 19F27]

Citation

Sato, Ken-ichi. On a problem of R. Brauer on zeta-functions of algebraic number fields. Proc. Japan Acad. Ser. A Math. Sci. 61 (1985), no. 10, 305--307. doi:10.3792/pjaa.61.305. https://projecteuclid.org/euclid.pja/1195514530


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References

  • [1] E. Artin: Uber eine neue Art von L-Reihen. Abh. Math. Sem. Univ. Hamburg, 3, 89-108 (1923).
  • [2] E. Artin: Zur Theorie der L-Reihen mit allgemeinen Gruppen-charakteren. ibid., 8, 292-306 (1930).
  • [3] R. Brauer: A note on zeta-functions of algebraic number fields. Acta Arith., 24, 325-327 (1973).
  • [4] J. C. Lagarias and A. M. Odlyzko: On computing Artin L-functions in the critical strip. Math. Comp., 33, 1081-1095 (1979).
  • [5] J. P. Serre: Linear Representations of Finite Groups. Springer (1977).
  • [6] K. Uchida: On Artin L-functions. Tohoku Math. J., 27, 75-81 (1975).
  • [7] R. W. van der Waall: A remark on the zeta-function of an algebraic number field. J. Reine Angew. Math., 266, 159-162 (1974).

See also

  • Part II: Ken-ichi Sato. On a problem of R. Brauer on zeta-functions of algebraic number fields, II. Proc. Japan Acad. Ser. A Math. Sci., Volume 63, Number 6 (1987), 212--214.