Some explicit zero-free regions for Hecke L-functions
DC Field | Value | Language |
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dc.contributor.author | Ahn, Jeoung-Hwan | - |
dc.contributor.author | Kwon, Soun-Hi | - |
dc.date.accessioned | 2021-09-05T02:22:10Z | - |
dc.date.available | 2021-09-05T02:22:10Z | - |
dc.date.created | 2021-06-15 | - |
dc.date.issued | 2014-12 | - |
dc.identifier.issn | 0022-314X | - |
dc.identifier.uri | https://scholar.korea.ac.kr/handle/2021.sw.korea/96576 | - |
dc.description.abstract | Let K be an algebraic number field of degree n over Q and let d(K) denote the absolute value of its discriminant. Let chi be a Hecke character on K with conductor F(chi). We let L(s,chi) denote the Hecke L-function associated with chi. Set A(chi) = d(K)N(K/Q)(F(chi)). In this paper we present some explicit zero-free regions for Hecke 1,L-functions. For example we prove the following results using Stechkin's device: If K not equal Q, the Dedekind zeta function zeta(K) (s) has at most one zero rho = beta + i gamma with beta > 1 - (2 log d(K))(-1) and vertical bar gamma vertical bar < (2 log d(K))(-1). This zero, if it exists, has to be real and simple; If x is a primitive Hecke character on K of order 2, then L(s,x) has at most one zero rho = beta + i gamma with beta > 1 - (4 log A(chi))(-1) and vertical bar gamma vertical bar < (4 log A chi)(-1). If such a zero exists, it has to be real and simple. Moreover, using approaches due to Heath-Brown and to Kadiri, we show that for a primitive Hecke character chi on K of order vertical bar chi vertical bar >= 3, L(s, chi) has no zero rho = beta + i gamma in the region beta > 1 - (15.10 log A chi)(-1) and vertical bar gamma vertical bar < 1/3 tan(pi/8). (C) 2014 Elsevier Inc. All rights reserved. | - |
dc.language | English | - |
dc.language.iso | en | - |
dc.publisher | ACADEMIC PRESS INC ELSEVIER SCIENCE | - |
dc.subject | DEDEKIND ZETA-FUNCTIONS | - |
dc.subject | DIRICHLET L-FUNCTIONS | - |
dc.subject | LEAST PRIME | - |
dc.subject | THEOREM | - |
dc.title | Some explicit zero-free regions for Hecke L-functions | - |
dc.type | Article | - |
dc.contributor.affiliatedAuthor | Ahn, Jeoung-Hwan | - |
dc.contributor.affiliatedAuthor | Kwon, Soun-Hi | - |
dc.identifier.doi | 10.1016/j.jnt.2014.06.008 | - |
dc.identifier.scopusid | 2-s2.0-84907379771 | - |
dc.identifier.wosid | 000341615200025 | - |
dc.identifier.bibliographicCitation | JOURNAL OF NUMBER THEORY, v.145, pp.433 - 473 | - |
dc.relation.isPartOf | JOURNAL OF NUMBER THEORY | - |
dc.citation.title | JOURNAL OF NUMBER THEORY | - |
dc.citation.volume | 145 | - |
dc.citation.startPage | 433 | - |
dc.citation.endPage | 473 | - |
dc.type.rims | ART | - |
dc.type.docType | Article | - |
dc.description.journalClass | 1 | - |
dc.description.journalRegisteredClass | scie | - |
dc.description.journalRegisteredClass | scopus | - |
dc.relation.journalResearchArea | Mathematics | - |
dc.relation.journalWebOfScienceCategory | Mathematics | - |
dc.subject.keywordPlus | DEDEKIND ZETA-FUNCTIONS | - |
dc.subject.keywordPlus | DIRICHLET L-FUNCTIONS | - |
dc.subject.keywordPlus | LEAST PRIME | - |
dc.subject.keywordPlus | THEOREM | - |
dc.subject.keywordAuthor | Dedekind zeta functions | - |
dc.subject.keywordAuthor | Hecke L-functions | - |
dc.subject.keywordAuthor | Zero-free regions for Dedekind zeta functions | - |
dc.subject.keywordAuthor | Zero-free regions for Hecke | - |
dc.subject.keywordAuthor | L-functions | - |
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