Confusing notation in "Introduction to the Construction of Class Fields"

Question

In "Introduction to the Construction of Class Fields" (by Harvey Cohn) there is this sentence in page 4: "We are hereby asserting that the previous results are all contained in the following statement
$ (1.8)$ $ p=x^2 + 4.4^ty^2 \Leftrightarrow p$ splits in $Q(i,j(2^{t+1}i)) (=k_{2.2^t}) $

Here $p$ is a prime and $j$ is the modular j-invariant. The previous results in which the sentence refers are:
$ p=x^2 + 4y^2 \Leftrightarrow p$ splits in $Q(i) (=k_{2}) $
$ p=x^2 + 16y^2 \Leftrightarrow p$ splits in $Q(i,\sqrt2) (=k_{4}) $
$ p=x^2 + 64y^2 \Leftrightarrow p$ splits in $Q(i,^4\sqrt2) (=k_{8}) $
$ p=x^2 + 256y^2 \Leftrightarrow p$ splits in $Q(i,^8\sqrt2\sqrt{1+\sqrt2}) (=k_{16}) $

I don't understand the notations $4.4^t$ and ${2.2^t}$ in (1.8). Shouldn't the equation be
$ p=x^2 + 4^ty^2 \Leftrightarrow p$ splits in $Q(i,j(2^{t+1}i)) (=k_{2^t}) $ ?

Am I missing some obvious point here?

Answer 1

I am pretty sure $4 . 4^t$ actually means $4 * 4^t$ or $4^{t+1}$, and that they are assuming $t >= 0$, instead of $t > 0$. But I agree with you they should make this explicit.