ISSN 0253-2778

CN 34-1054/N

Open AccessOpen Access JUSTC

Ramification in relative quadratic extensions and fundamental units of real quadratic fields

Cite this:
https://doi.org/10.3969/j.issn.0253-2778.2015.08.001
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  • Author Bio:

    WANG Bing, male, born in 1982, PhD candidate. Research field: algebraic number theory. E-mail: wangbinx@mail.ustc.edu.cn

  • Corresponding author: ZHANG Zhe
  • Received Date: 10 November 2014
  • Rev Recd Date: 07 July 2015
  • Publish Date: 31 August 2015
  • Let F=Q(d) be a real quadratic field and ε=x+yd the fundamental unit of F satisfying NF/Q(ε)=1. Some connections between the ramification properties for dyadic prime ideals in quadratic extension F(ε)/F and congruence properties of x, y were established. As a corollary, some congruence properties about x, y were given when d=p1…pr or 2p1…pr with p1≡…≡pr≡1 mod 4 being distinct prime numbers.
    Let F=Q(d) be a real quadratic field and ε=x+yd the fundamental unit of F satisfying NF/Q(ε)=1. Some connections between the ramification properties for dyadic prime ideals in quadratic extension F(ε)/F and congruence properties of x, y were established. As a corollary, some congruence properties about x, y were given when d=p1…pr or 2p1…pr with p1≡…≡pr≡1 mod 4 being distinct prime numbers.
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