On the reduction of binary quadratic forms

Creative Commons License

ZEYTİN A.

PUBLICATIONES MATHEMATICAE-DEBRECEN, cilt.89, ss.203-221, 2016 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 89
  • Basım Tarihi: 2016
  • Doi Numarası: 10.5486/pmd.2016.7470
  • Dergi Adı: PUBLICATIONES MATHEMATICAE-DEBRECEN
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.203-221
  • Anahtar Kelimeler: carks, binary quadratic forms, reduction theory, representation problem of binary quadratic forms, minimum problem of binary quadratic forms
  • Galatasaray Üniversitesi Adresli: Evet

Özet

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.