Zeros of partial sums of the Dedekind zeta function of a cyclotomic field

JOURNAL OF NUMBER THEORY

卷:136

Article

Ledoan, Andrew¹  Roy, Arindam²  Zaharescu, Alexandru² 

[1] Univ Tennessee, Dept Math, Chattanooga, TN 37403 USA

[2] Univ Illinois, Dept Math, Urbana, IL 61801 USA

关键词: Dedekind zeta function;    Dirichlet polynomial;    Distribution of zeros;   

DOI  :  10.1016/j.jnt.2013.09.003

来源: Elsevier

【 摘 要 】

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 series (GRAPHICS) where the sum is to be taken over nonzero integral ideals a of K and Hall denotes the absolute norm of a. Specifically, we establish the zero-free regions for sigma K,x(s) and estimate the number of zeros of sigma K,X(S) up to height T. (C) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

Free