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 -