Estimate of a Trigonometrical Sum Involving Naturals with Binary Decompositions of a Special Kind

Abstract

Let ${\mathbb{N}}_0$ be a class of natural numbers whose binary decompositions has even number of 1. We estimate of the sum $\sum _{n\in {\mathbf{N}}_0,n\le X}\exp (2\pi i\alpha n^2)$.

5 pages