Beschreibung:
In 1966, Shanks and Schmid investigated the asymptotic behavior of the number of positive integers less than or equal to x which are represented by the quadratic form X 2 + n Y 2, n ≥ 1. Based on some numerical computations, they observed that the constant occurring in the main term appears to be the largest for n = 2. In this paper, we prove that in fact this constant is unbounded as one runs through fundamental discriminants with a fixed number of distinct prime divisors.