Let N(t,ρ) be the number of lattice points in a thin elliptical annuli.
We assume the aspect ratio β of the ellipse is transcendental and
Diophantine in a strong sense (this holds for {\em almost all} aspect ratios).
The variance of N(t,ρ) is t(8πβ⋅ρ). We show that if
ρ shrinks slowly to zero then the distribution of the normalized counting
function 8πβ⋅tρN(t,ρ)−A(2tρ+ρ2) is Gaussian, where A is the area of the ellipse. The case of
\underline{circular} annuli is due to Hughes and Rudnick