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

  • 1.

    School of Mathematical Sciences, University of Science and Technology of China, Hefei 230026, China

  • 2.

    School of Mathematics and Statistics, Xidian University, Xian 710126, China

Cite this: JUSTC, 2015, 45(8): 623-626
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: November 09, 2014
  • Revised Date: July 06, 2015
  • Published Date: August 30, 2015
    Abstract
  • 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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