Gitterpunkte in Lemniskatenscheiben

Let G (R) denote the number of lattice points (,) **Z² in the domain B(R) bounded by the lemniscate (x²+y²)²=2R² (x²–y²) and put P(R)=G(R)-R²(R² being the area of B(R)). The purpose of this paper is to determine the order of magnitude of P(R) for large R by proving the asymptotic relation (3). An analogous result is given for the eight curve x⁴=R² (x²–y²).