Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4593918 | Journal of Number Theory | 2014 | 16 Pages |
Abstract
In this article, we study the zeros of the partial sums of the Dedekind zeta function of a cyclotomic field K defined by the truncated Dirichlet seriesζK,X(s)=ââaâ⩽X1âaâs, where the sum is to be taken over nonzero integral ideals a of K and âaâ denotes the absolute norm of a. Specifically, we establish the zero-free regions for ζK,X(s) and estimate the number of zeros of ζK,X(s) up to height T.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Andrew Ledoan, Arindam Roy, Alexandru Zaharescu,