4 problems

Let $k$ be a number field, let $S$ be a finite set of places, and let $L_1,\dots,L_q$ be linear forms in $r+1$ variables with coefficients in $k$ determining $q$ hyperplanes in gen…

The main inequalities for points of bounded degree. There exists a constant $\mathrm{c}(r,d)>0$, depending only on $r$ and $d$, such that, for every fixed $\delta>0$, if…

Let $S$ be a finite set of places of a number field $k$. Let $H_1,\ldots,H_q$ be hyperplanes over $k$ in general position in $\mathbb{P}^n$, and set … Let $\delta$ be a positive in…

Let $k$ be a number field, let $S$ be a finite set of places of $k$, and let $H_{0,v},\ldots,H_{n,v}$ be hyperplanes in $\mathbb{P}^n$ for each $v\in S$. For a point $P$ of bounded…