TY - JOUR

T1 - Zeros of partial sums of the Dedekind zeta function of a cyclotomic field

AU - Ledoan, Andrew

AU - Roy, Arindam

AU - Zaharescu, Alexandru

PY - 2014/3

Y1 - 2014/3

N2 - 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)=∑{norm of matrix}a{norm of matrix}≤X1{norm of matrix}a{norm of matrix}s, where the sum is to be taken over nonzero integral ideals a of K and {norm of matrix}a{norm of matrix} 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.

AB - 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)=∑{norm of matrix}a{norm of matrix}≤X1{norm of matrix}a{norm of matrix}s, where the sum is to be taken over nonzero integral ideals a of K and {norm of matrix}a{norm of matrix} 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.

KW - Dedekind zeta function

KW - Dirichlet polynomial

KW - Distribution of zeros

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U2 - 10.1016/j.jnt.2013.09.003

DO - 10.1016/j.jnt.2013.09.003

M3 - Article

AN - SCOPUS:84888038828

SN - 0022-314X

VL - 136

SP - 118

EP - 133

JO - Journal of Number Theory

JF - Journal of Number Theory

ER -