All Questions

I run into this inequality $$ (a + b)^{1 - \epsilon} \;a < b $$ where $a \in \mathbb{Z}^+$ and $\epsilon \in (0, 1)$. What value (w.r.t $a$ and $\epsilon$) should I set $b$ equal to such that this ...

A famous conjecture posed by Littlewood and solved by O. McGehee, L. Pigno, and B. Smith(in their article, Hardy's inequality and the $L_1$-norm of exponential sums) and S. V. Konyagin independently ...

Let $M$ be some large real number and $\delta>0$. I would like to estimate the number of solutions for the inequality $$|\sqrt{n_1}+\sqrt{n_2}-\sqrt{n_3}-\sqrt{n_4}|<\delta\sqrt{M},$$ where $...