Published September 2017
| public
Journal Article
Smooth L^2 distances and zeros of approximations of Dedekind zeta functions
Abstract
We consider a family of approximations of the Dedekind zeta function ζK(s) of a number field K/Q. Weighted L^2-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 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.
Additional Information
© 2017 Springer-Verlag Berlin Heidelberg. Received: 01 June 2015; Accepted: 19 December 2016; First Online: 17 January 2017. The authors are grateful to the referee for many useful comments and suggestions.Additional details
- Eprint ID
- 78204
- DOI
- 10.1007/s00229-016-0911-6
- Resolver ID
- CaltechAUTHORS:20170614-104233433
- Created
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2017-06-14Created from EPrint's datestamp field
- Updated
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2021-11-15Created from EPrint's last_modified field