Journal of Mathematical Sciences

, Volume 150, Issue 3, pp 2115–2122

Mean values connected with the Dedekind zeta function


DOI: 10.1007/s10958-008-0126-9

Cite this article as:
Fomenko, O.M. J Math Sci (2008) 150: 2115. doi:10.1007/s10958-008-0126-9


For a cubic extension K3/ℚ, which is not normal, new results on the behavior of mean values of the Dedekind zeta function of the field K3 in the critical strip are obtained.

Let M(m) denote the number of integral ideals of the field K3 of norm m. For the sums
$$\sum\limits_{m \leqslant x} {M(m)^2 } and \sum\limits_{m \leqslant x} {M(m)^3 } $$
asymptotic formulas are derived. Previously, only upper bounds for these sums were known. Bibliography: 23 titles.

Copyright information

© Springer Science+Business Media, Inc. 2008

Authors and Affiliations

  1. 1.St.Petersburg Department of the Steklov Mathematical InstituteSt.PetersburgRussia

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