Abstract :
Let f be an indefinite ternary integral quadratic form and let q be a nonzero integer such that −q det(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 N(T, f, q)not, vert, similarcEHL(T, f, q) as T→∞, where EHL(T, f, q) is the Hardy–Littlewood expectation (the product of local densities) and 0less-than-or-equals, slantcless-than-or-equals, slant2. We give examples of f and q such that c takes the values 0, 1, 2.
