All Questions

Define $\mathfrak{m}$ as the union of the minor arcs of the form $|\alpha-\frac{a}{q}|\leq 1/qQ$, with $(a,q)=1$ and $Q_0<q\leq Q$, with $Q_0\geq N/Q$, for a certain $N\geq Q$ large. Is it ...

Let $n_1,\dots,n_k$ be a set of $k$ natural numbers less than $N$, with $k = (1- \delta) \log_2 N$ for $\delta$ relatively small. Let $e(x) = e^{ 2\pi i x}$, as usual. Assume that $$\int_0^1\prod_{j=1}...

Let $$ f(x,N) = \sum_{0 \leq n\leq N} e(x n^2).$$ Weyl's inequality gives an estimate for $f(x,N)$ when $x$ is near a rational with small denominator. My question is: What estimates are ...

In section 11 of this paper by Thanigasalam, it says "... we get $G(10)\le 105$, and this implies that $H(10) \le 107$". However, it is very unclear how this follows. Why is it the case that $G(10)\le ...