Abstract
We consider a family of approximations of the Dedekind zeta function \(\zeta _K(s)\) of a number field \(K/\mathbb {Q}\). Weighted \(L^2\)-norms of the difference of two such approximations of \(\zeta _K(s)\) are computed. We work with a weight which is a compactly supported smooth function. Mean square estimates for the difference of approximations of \(\zeta _K(s)\) can be obtained from such weighted \(L^2\)-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.
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Li, J., Nastasescu, M., Roy, A. et al. Smooth \(L^2\) distances and zeros of approximations of Dedekind zeta functions. manuscripta math. 154, 195–223 (2017). https://doi.org/10.1007/s00229-016-0911-6
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DOI: https://doi.org/10.1007/s00229-016-0911-6