Limit theorems for toral translations

The survey’s statements (Theorem 10 and Theorem 18) give the normalization r^{(d−1)/2} N^{(d−1)/(2d)} and the explicit limit L_Ω(L,θ,b,b′) in equations (22)–(23), with a proof sketch based on Fourier localization, stationary phase, and equidistribution of expanding translates in the space of lattices . The candidate solution reproduces the overall strategy and the correct limit functional, but it uses the wrong power of N throughout (it claims N^{(d−1)/2} instead of N^{(d−1)/(2d)}), which contradicts the paper’s result. It also asserts L^2-convergence of the lattice series, whereas the paper cites almost-everywhere convergence; the L^2 claim is not justified here. Hence: paper correct; model wrong.