SOME REMARKS ON INDEFINITE BINARY QUADRATIC FORMS AND QUADRATIC IDEALS

Tekcan A.

HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS, vol.36, no.1, pp.27-36, 2007 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 36 Issue: 1
  • Publication Date: 2007
  • Journal Name: HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), TR DİZİN (ULAKBİM)
  • Page Numbers: pp.27-36
  • Bursa Uludag University Affiliated: Yes

Abstract

Let delta denote a real quadratic irrational with trace t = delta + (delta) over bar and norm n = delta(delta) over bar Given a real quadratic irrational gamma epsilon Q(delta), there are rational integers P and Q such that gamma = P+delta/Q with Q|(delta + P) ((delta) over bar + P). Hence for each gamma = P+delta/Q, there is a corresponding ideal I-gamma = [Q, P + delta], and an indefinite binary quadratic form F-gamma(x, y) = Q(x + delta y) (x + (delta) over bary) of discriminant Delta = t(2) - 4n.