On the reduction of binary quadratic forms

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ZEYTİN A.

PUBLICATIONES MATHEMATICAE-DEBRECEN, vol.89, pp.203-221, 2016 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 89
  • Publication Date: 2016
  • Doi Number: 10.5486/pmd.2016.7470
  • Journal Name: PUBLICATIONES MATHEMATICAE-DEBRECEN
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.203-221
  • Keywords: carks, binary quadratic forms, reduction theory, representation problem of binary quadratic forms, minimum problem of binary quadratic forms
  • Galatasaray University Affiliated: Yes

Abstract

We give an interpretation of the reduction algorithm of Gauss in terms of carks, which are certain types of infinite ribbon graphs (or infinite dessins). We then describe an alternative reduction which is slightly faster than Gauss'. We also solve the minimal value problem and describe an algorithmic solution to the representation problem of indefinite binary quadratic forms.