EUDML

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.

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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

Proper cycles of indefinite quadratic forms and their right neighbors

The connection between quadratic forms and the extended modular group

Advanced Search

Formula preview

Currently displaying 1 – 7 of 7

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

Proper cycles of indefinite quadratic forms and their right neighbors

The connection between quadratic forms and the extended modular group

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 $S_{4} (Γ_{0} (47), 1)$ .