Estimate of a Trigonometrical Sum Involving Naturals with Binary   Decompositions of a Special Kind
  Let $\mathbb{N}_0$ be a class of natural numbers whose binary decompositions has even number of 1. We estimate of the sum $\sum\limits_{n\in \mathbf{N}_0,n\le X}\exp(2\pi i \alpha n^2)$. 
Karen M. Eminyan