We consider a family of approximations of the Dedekind zeta function ζK(s) of a number field K/ Q. Weighted L2-norms of the difference of two such approximations of ζK(s) are computed. We work with a weight which is a compactly supported smooth function. Mean square estimates for the difference of approximations of ζK(s) can be obtained from such weighted L2-norms. Some results on the location of zeros of a family of approximations of Dedekind zeta functions are also derived. These results extend results of Gonek and Montgomery on families of approximations of the Riemann zeta-function.
- Primary 11M41
ASJC Scopus subject areas