Special Issue "Axioms in Number Theory"

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A special issue of Axioms (ISSN 2075-1680).

Deadline for manuscript submissions: closed (15 November 2012)

Special Issue Editor

Guest Editor
Prof. Dr. Mirela Stefanescu (Website)

Faculty of Sciences, Ovidius University of Constanza, Mamaia 124, 900527 Constanta, Romania
Interests: axiomatic theories in algebra; group theory; field and ring theory; number theory; axiomatic methods; axiomatization

Keywords

  • 11Axx, specially 11A05
  • 11Dxx
  • 11Exx
  • 11Fxx

Published Papers (1 paper)

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Research

Open AccessArticle On the Content Bound for Real Quadratic Field Extensions
Axioms 2013, 2(1), 1-9; doi:10.3390/axioms2010001
Received: 31 October 2012 / Revised: 18 December 2012 / Accepted: 20 December 2012 / Published: 28 December 2012
PDF Full-text (172 KB) | HTML Full-text | XML Full-text
Abstract
Let K be a finite extension of and let S = {ν} denote the collection of K normalized absolute values on K. Let V K + denote the additive group of adeles over K and let c : [...] Read more.
Let K be a finite extension of and let S = {ν} denote the collection of K normalized absolute values on K. Let V K + denote the additive group of adeles over K and let c : V K + 0 denote the content map defined as c( { a v } ) = vs v( a v ) for { a v } V K + . A classical result of J. W. S. Cassels states that there is a constant c > 0 depending only on the field K  with the following property: if { a v } V K + with c( { a v } ) > c , then there exists a non-zero element b  ∈ K for which v(b)v( a v ), v S . Let cK be the greatest lower bound of the set of all c that satisfy this property. In the case that K is a real quadratic extension there is a known upper bound for cK due to S. Lang. The purpose of this paper is to construct a new upper bound for cK in the case that K has class number one. We compare our new bound with Lang’s bound for various real quadratic extensions and find that our new bound is better than Lang’s in many instances. Full article
(This article belongs to the Special Issue Axioms in Number Theory)

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