Lattice points problem, equidistribution and ergodic theorems for certain arithmetic spheres

Alex Iosevich, Bartosz Langowski, Mariusz Mirek +1

We establish an asymptotic formula for the number of lattice points in the sets \[ \mathbf S_{h_1, h_2, h_3}(λ): =\{x\in\mathbb Z_+^3:\lfloor h_1(x_1)\rfloor+\lfloor h_2(x_2)\rfloo…