The minima of indefinite binary quadratic forms

Let f(x,y) be an indefinite binary quadratic form, D(f) its discriminant, m(f) the infimum of |f(x,y)| over all integers x, y not both zero, and put μ(f) = m(f)D(f)−12 role=presentation style=font-size: 90%; display: inline-block; position: relative;>$\text{μ(f) = m(f)D(f)}{}^{\mathrm{<mtext>-1</mtext><mtext>2</mtext>}}$$\text{μ(f) = m(f)D(f)}{}^{\mathrm{<mtext>-1</mtext><mtext>2</mtext>}}$. In this paper we shall prove the existence of countably many disjoint open intervals I_i contained in 0 ≤ x ≤13 role=presentation style=font-size: 90%; display: inline-block; position: relative;>$\text{0 ≤ x ≤}\text{1}\text{3}$$\text{0 ≤ x ≤}\text{1}\text{3}$ such that there is no f with μ(f) in I_i (j = 1,2,…), and such that for any interval I containing two intervals I_j, I_k, there is an f with μ(f) in I.