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The mean-value of the Artin L-series and its derivative of a cubic field

Published online by Cambridge University Press:  18 May 2009

Lenard Weinstein
Lenard Weinstein
Affiliation:
Department of Mathematics, Boston University, Boston, Massachusetts 02215
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Let K be a non-abelian cubic field of discriminant D, and ζK(s) its Dedekind zeta-function. Set ψ(s) = ζk(s)/ζ(s). Then it is known that ψ(s) is the Artin L-series associated with the field K. It is also known that ψ(s) is an entire function of order 1.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 21 , Issue 1 , January 1980 , pp. 9 - 18
Copyright
Copyright © Glasgow Mathematical Journal Trust 1980

References

REFERENCES

1.Barrucand, P., Quelques propriétés des coefficients des séries L associées aux corps cubiques, C.R. Acad. Paris Sci. Sér. A–B 273 (1971), A960–A963.Google Scholar
2.Motohashi, Y., A note on the mean value of the Dedekind zeta-function of the quadratic field, Math. Ann. 188 (1970), 123–127.Google Scholar
3.Titchmarsh, E. C., The mean-value of the zeta-function on the critical line, Proc. London Math. Soc. (2) 27 (1928), 137–150.CrossRefGoogle Scholar
4.Titchmarsh, E. C., The theory of the Riemann zeta-function (Oxford: Clarendon Press, 1951).Google Scholar
5.Weinstein, L., The mean value of the derivative of the Dedekind zeta-function of a real quadratic field, Mathematika 24 (1977), 226–236.Google Scholar