On indefinite ternary 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...

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).

On successive minima of indefinite quadratic forms

On Indefinite Binary Quadratic Forms and Quadratic Ideals

We consider some properties of indefinite binary quadratic forms F (x, y) = ax +bxy−y of discriminant ∆ = b +4a, and quadratic ideals I = [a, b−√∆ ]. AMS Mathematics Subject Classification (2000): 11E04, 11E12, 11E16

On Representation Numbers of Ternary Quadratic Forms

The representation number rQ(m) is the number of integral representations of the integer m by the integral quadratic form Q over a global number field. The main obstruction to obtaining information about representation numbers is that global integrally inequevalent forms might nevertheless be equivalent over every local field (i.e. in the same genus). This failure of the localglobal principle s...