3 problems

Let $\alpha$ be an irrational rotation parameter, let $\psi_M(x)=\psi(Mx)$, and define the twisted Birkhoff sum $S_N(\psi_M\phi)$ in the setting of lemma 84. Uniform twisted-sum co…

Let $S_N\frac{1}{\left\Vert x\right\Vert }$ be the estimate in equation $\mathrm{EstLBSymm}$, and let $S_{b_nq_n}\frac{1}{\left\Vert x\right\Vert }$ be the current estimate, with l…

Variance growth conjecture. The variance satisfies $\log M\ll B_M^2\ll\log M$. This accompanies a proved central limit theorem with the natural centering and scaling; the source la…