THE BASE POINTS OF INDEFINITE QUADRATIC FORMS IN THE CYCLE AND PROPER CYCLE OF AN INDEFINITE QUADRATIC FORM

Authors : A. TEKCAN

Pages : 101-114

View : 14 | Download : 6

Publication Date : 2007-02-01

Article Type : Research Paper

Abstract :Let F = insert ignore into journalissuearticles values(a, b, c); be an indefinite quadratic form of discriminant ∆ > 0. In the first section, we give some preliminaries from binary quadratic forms. In the second section, we derive some results concerning the base points of indefinite quadratic forms in the cycle and proper cycle of F using the transformations τ insert ignore into journalissuearticles values(F); = insert ignore into journalissuearticles values(−a, b, −c);, ξinsert ignore into journalissuearticles values(F); = insert ignore into journalissuearticles values(c, b, a);, χinsert ignore into journalissuearticles values(F); = insert ignore into journalissuearticles values(−c, b, −a);, ψinsert ignore into journalissuearticles values(F); = insert ignore into journalissuearticles values(−a, −b, −c);, and the right neighbor R i insert ignore into journalissuearticles values(F); of F for i ≥ 0.
Keywords : Quadratic form, Indefinite form, Cycle, Proper cycle, Right neighbor, Base point