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math.DS2021
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…
math.CA2021
Restriction of exponential sums to hypersurfaces
Ciprian Demeter, Bartosz Langowski
We prove moment inequalities for exponential sums with respect to singular measures, whose Fourier decay matches those of curved hypersurfaces. Our emphasis will be on proving esti…