Equidistribution of lattice points on spheres in dimensions $d \ge 4$ (Pommerenke's theorem)

Question

I am looking for either an English translation of:

Pommerenke, C.: Über die Gleichverteilung von Gitterpunkten auf m-dimensionalen Ellipsoiden. Acta Arith. 5, 227-257 (1959)

Or a reference in English (preferably a book) that proves:

Pommerenke's Theorem.

1. In dimension $d \ge 5$ the points on the sphere $\mathcal{S}^{d-1}$ which correspond to sums of $d$ squares $x_1^2 + \ldots + x_d^2 = n$ after dividing $(x_1, \ldots, x_d)$ by $\sqrt n$ are equidistributed as $n \to \infty$.
2. In dimension $d = 4$ the above is true with certain additional restrictions on $n$.

(Pommerenke's original theorem is about ellipsoids; I only need the special case of spheres.)

I have found what seems to be the correct theorem in H. Iwaniec's Topics in Classical Automorphic Forms, chapter 11.6; however, this book seems a bit too difficult for me.

Answer 1

My notes http://www.math.umn.edu/~garrett/m/mfms/notes_2013-14/10_thetas_equi.pdf linked-to from http://www.math.umn.edu/~garrett/m/mfms/ prove the result when dimension is divisible by 8.

About history and priorities: my impression was that Kloosterman had "known" the cases of dimension 5 and above by 1926. In any case, there is a bibliography in that notes-fragment.