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

2013/07/31 by Andrew Ledoan, Ledoan, Andrew, Arindam Roy +3
Mathematics · #Advanced Mathematical Identities #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1308.0065

openalex publication_date 2013/07/31 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28

Abstract

In this article, we study the zeros of the partial sums of the Dedekind zeta\nfunction of a cyclotomic field K defined by the truncated Dirichlet series n
zeta_{K, X} (s)\n =
sum_
|
mathfraka
|
leq X
frac1
|
mathfraka
|^s, where the\nsum is to be taken over nonzero integral ideals mathfraka of K and\n\‖ mathfraka\‖ denotes the absolute norm of mathfraka. Specifically,\nwe establish the zero-free regions for \ζ_{K, X} (s) and estimate the\nnumber of zeros of \ζ_{K, X} (s) up to height T.\n

Related

• Zeros of partial sums of L-functions
• New zero-free regions for Dedekind zeta-functions at small and large ordinates
• Counting zeros of Dedekind zeta functions
• Estimating the number of zeros of Dedekind zeta-functions
• On density of the zeros of Dedekind zeta-functions