Proper cycles of indefinite quadratic forms and their right neighbors

Tekcan A.

APPLICATIONS OF MATHEMATICS, vol.52, no.5, pp.407-415, 2007 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 52 Issue: 5
  • Publication Date: 2007
  • Doi Number: 10.1007/s10492-007-0023-4
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.407-415
  • Bursa Uludag University Affiliated: Yes


In this paper we consider proper cycles of indefinite integral quadratic forms F = (a, b, c) with discriminant A. We prove that the proper cycles of F can be obtained using their consecutive right neighbors R-i(F) for i >= 0. We also derive explicit relations in the cycle and proper cycle of F when the length I of the cycle of F is odd, using the transformations tau(F) = (-a, b, -c) and chi(F) = (-c, b, -a).