Asymmetric minima of indefinite ternary quadratic forms

On successive minima of indefinite quadratic forms

On Representations of Integers by Indefinite Ternary Quadratic Forms

Let f be an indefinite ternary integral quadratic form and let q be a nonzero integer such that −qdet(f) is not a square. Let N(T, f, q) denote the number of integral solutions of the equation f(x) = q where x lies in the ball of radius T centered at the origin. We are interested in the asymptotic behavior of N(T, f, q) as T → ∞. We deduce from the results of our joint paper with Z.Rudnick that...

Quadratic Minima and Modular Forms

1991 Mathematics Subject Classi cation: 11F11, 11E20.

Effective Estimates on Indefinite Ternary Forms

We give an effective proof of a theorem of Dani and Margulis regarding values of indefinite ternary quadratic forms at primitive integer vectors. The proof uses an effective density-type result for orbits of the groups SO(2, 1) on SL(3,R)/ SL(3,Z).

Neighbors of Indefinite Binary Quadratic Forms

In this paper, we derive some algebraic identities on right and left neighbors R(F ) and L(F ) of an indefinite binary quadratic form F = F (x, y) = ax + bxy + cy of discriminant Δ = b − 4ac. We prove that the proper cycle of F can be given by using its consecutive left neighbors. Also we construct a connection between right and left neighbors of F . Keywords—Quadratic form, indefinite form, cy...