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Proper cycles of indefinite quadratic forms and their right neighbors

Ahmet Tekcan — 2007

Applications of Mathematics

In this paper we consider proper cycles of indefinite integral quadratic forms $F = (a, b, c)$ with discriminant $Δ$ . We prove that the proper cycles of $F$ can be obtained using their consecutive right neighbors $R^{i} (F)$ for $i \geq 0$ . We also derive explicit relations in the cycle and proper cycle of $F$ when the length $l$ of the cycle of $F$ is odd, using the transformations $τ (F) = (- a, b, - c)$ and $χ (F) = (- c, b, - a)$ .

The connection between quadratic forms and the extended modular group

Ahmet Tekcan; Osman Bizim — 2003

Mathematica Bohemica

In this paper some properties of quadratic forms whose base points lie in the point set $F_{\bar{Π}}$ , the fundamental domain of the modular group, and transforming these forms into the reduced forms with the same discriminant $Δ < 0$ are given.

On indefinite binary quadratic forms and quadratic ideals.

Tekcan, Ahmet — 2008

Novi Sad Journal of Mathematics

The cubic congruence $x^{3} + a x^{2} + b x + c \equiv 0 (mod p)$ and binary quadratic forms $F (x, y) = a x^{2} + b x y + c y^{2}$ . II.

Tekcan, Ahmet — 2010

Acta Universitatis Apulensis. Mathematics - Informatics

Quadratic Diophantine equation $x^{2} - (t^{2} - t) y^{2} - (4 t - 2) x + (4 t^{2} - 4 t) y = 0$ .

Özkoç, Arzu; Tekcan, Ahmet — 2010

Bulletin of the Malaysian Mathematical Sciences Society. Second Series

On the number of representations of positive integers by quadratic forms as the basis of the space $S_{4} (Γ_{0} (47), 1)$ .

Tekcan, Ahmet; Bizim, Osman — 2004

International Journal of Mathematics and Mathematical Sciences

Pell Form and Pell Equation via Oblong Numbers

Tekcan, Ahmet; Özkoç, Arzu — 2013

Serdica Mathematical Journal

2010 Mathematics Subject Classification: 11D09, 11D25, 11D41, 11D72, 11E16, 11E18.

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Currently displaying 1 – 7 of 7

Proper cycles of indefinite quadratic forms and their right neighbors

The connection between quadratic forms and the extended modular group

On indefinite binary quadratic forms and quadratic ideals.

The cubic congruence $x^{3} + a x^{2} + b x + c \equiv 0 (mod p)$ and binary quadratic forms $F (x, y) = a x^{2} + b x y + c y^{2}$ . II.

Quadratic Diophantine equation $x^{2} - (t^{2} - t) y^{2} - (4 t - 2) x + (4 t^{2} - 4 t) y = 0$ .

On the number of representations of positive integers by quadratic forms as the basis of the space $S_{4} (Γ_{0} (47), 1)$ .

Pell Form and Pell Equation via Oblong Numbers

Advanced Search

Formula preview

Currently displaying 1 – 7 of 7

Proper cycles of indefinite quadratic forms and their right neighbors

The connection between quadratic forms and the extended modular group

On indefinite binary quadratic forms and quadratic ideals.

The cubic congruence x 3 + a x 2 + b x + c ≡ 0 ( mod p ) and binary quadratic forms F ( x , y ) = a x 2 + b x y + c y 2 . II.

Quadratic Diophantine equation x 2 - ( t 2 - t ) y 2 - ( 4 t - 2 ) x + ( 4 t 2 - 4 t ) y = 0 .

On the number of representations of positive integers by quadratic forms as the basis of the space S 4 ( Γ 0 ( 47 ) , 1 ) .

Pell Form and Pell Equation via Oblong Numbers

The cubic congruence $x^{3} + a x^{2} + b x + c \equiv 0 (mod p)$ and binary quadratic forms $F (x, y) = a x^{2} + b x y + c y^{2}$ . II.

Quadratic Diophantine equation $x^{2} - (t^{2} - t) y^{2} - (4 t - 2) x + (4 t^{2} - 4 t) y = 0$ .

On the number of representations of positive integers by quadratic forms as the basis of the space $S_{4} (Γ_{0} (47), 1)$ .