Cooper and Lam's conjecture for generalized Bell ternary quadratic forms

Bell's theorem determines the counting function of the ternary quadratic forms x2+by2+cz2x2+by2+cz2, with b,c∈{1,2,4,8}b,c∈{1,2,4,8}, in terms of the number r3(n)r3(n) of representations of n   as a sum of three squares. Based on it we verify Cooper and Lam's conjecture for them. This result includes two new cases so far left open. Additionally, we show that the forms (b,c)=(2,16)(b,c)=(2,16) and (b,c)=(8,16)(b,c)=(8,16) are generalized Bell forms in the sense that their counting functions depend only upon r3(n)r3(n). These forms satisfy Cooper and Lam's conjecture and solve two further open cases.