On Representations of Integers by Indefinite Ternary Quadratic Forms
نویسندگان
چکیده
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 N(T, f, q) ∼ cEHL(T, f, q) as T → ∞, where EHL(T, f, q) is the Hardy-Littlewood expectation (the product of local densities) and 0 ≤ c ≤ 2. We give examples of f and q such that c takes values 0,1,2. 0. Introduction Let f be a nondegenerate indefinite integral-matrix quadratic form of n variables: f(x1, . . . , xn) = n
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