Some criteria on invariant values

Isikay S., Pekin A.

MAEJO INTERNATIONAL JOURNAL OF SCIENCE AND TECHNOLOGY, vol.12, no.2, pp.101-111, 2018 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 12 Issue: 2
  • Publication Date: 2018
  • Journal Name: MAEJO INTERNATIONAL JOURNAL OF SCIENCE AND TECHNOLOGY
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.101-111
  • Keywords: invariant value, continued fraction, class number, real quadratic field, REAL QUADRATIC FIELDS, FUNDAMENTAL UNITS, EXPLICIT REPRESENTATION, CLASS-NUMBERS, FORM
  • Istanbul University Affiliated: Yes

Abstract

Let K = Q(root d) be a real quadratic field, where d is a positive square-free integer congruent to 1 modulo 4. In this paper we determine the first term of the symmetric part of the continued fraction expansion of the integral basis element omega(d) = (1 + root d)/2. Furthermore, we obtain a necessary and sufficient condition for Yokoi's d-invariant value to be zero and present some numerical results on the class number of such real quadratic fields.