Hostname: page-component-586b7cd67f-l7hp2 Total loading time: 0 Render date: 2024-12-01T00:03:32.813Z Has data issue: false hasContentIssue false
  • English
  • Français

The mean value of the derivative of the Dedekind zeta-function of a real quadratic field

Published online by Cambridge University Press:  26 February 2010

Lenard Weinstein
Lenard Weinstein
Affiliation:
Department of Mathematics, Boston University, Boston, Massachusetts 02215
Get access

Extract

Denote by ζk′(S), the derivative of the Dedekind zeta-function associated with the real quadratic field K. Then it is known that

where ζ(S) is the Riemann zeta-function, and L(s, x) is the Dirichlet L-series associated with the Legendre symbol X. Moreover, we have the functional equation

where D is the discriminant of K.

Type
Research Article
Information
Mathematika , Volume 24 , Issue 2 , December 1977 , pp. 226 - 236
Copyright
Copyright © University College London 1977

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Motohashi, Y.. “A note on the mean value of the Dedekind zeta-function of the quadratic field”, Math. Ann. 188 (1970) 123–127.CrossRefGoogle Scholar
2.Titchmarsh, E. C.. “The mean-value of the zeta-function on the critical line”, Proc. London Math. Soc, (2) 28 (1928), 137–150 (1928).CrossRefGoogle Scholar
3.Titchmarsh, E. C.. The theory of the Riemartn zeta-function, (Oxford, Clarendon Press, 1951).Google Scholar