arXiv subjects

A. Anas Chentouf

Publications and source records attributed to A. Anas Chentouf.

4 recordsLinked to original sources

arXiv2023

Tetrahedra tiling problem

Kedlaya, Kolpakov, Poonen, and Rubinstein classified tetrahedra all of whose dihedral angles are rational multiples of $π$ into two one-parameter families (a Hill family and a new family) and $59$ sporadic tetrahedra. In this paper, we consider which of them tile space; we show that every member of the Hill family, exactly one member of the new family, and at most $40$ sporadic tetrahedra tile space. As a corollary, we disprove the converse of Debrunner's theorem, showing that not all Dehn invariant zero tetrahedra tile space.

math.MG↗

arXiv2023

Dehn invariant zero tetrahedra

We survey literature on all known families and examples of Dehn invariant zero tetrahedra. We also contribute two previously unknown families of Dehn invariant zero tetrahedra. Following a suggestion of Dill and Habegger, we show that there are finitely many Dehn invariant zero tetrahedra whose dihedral angles have a five-dimensional span over $\mathbb{Q}$, a first step towards classifying all Dehn invariant zero tetrahedra.

math.MG↗

arXiv2023

Patterns of primes in joint Sato--Tate distributions

For $j=1,2$, let $f_j(z) = \sum_{n=1}^{\infty} a_{j}(n) e^{2πi nz}$ be a holomorphic, non-CM cuspidal newform of even weight $k_j \ge 2$ with trivial nebentypus. For each prime $p$, let $θ_{j}(p)\in[0,π]$ be the angle such that $a_j(p) = 2p^{(k-1)/2} \cos θ_{j}(p)$. The now-proven Sato--Tate conjecture states that the angles $(θ_j(p))$ equidistribute with respect to the measure $dμ_{\mathrm ST} = \frac{2}π\sin^2θ\,dθ$. We show that, if $f_1$ is not a character twist of $f_2$, then for subintervals $I_1,I_2 \subset [0,π]$, there exist infinitely many bounded gaps between the primes $p$ such that $θ_1(p) \in I_1$ and $θ_2(p) \in I_2$. We also prove a common generalization of the bounded gaps with the Green--Tao theorem.

math.NT↗

arXiv2021

Linear Recurrences of Order at Most Two in Small Divisors

Given a positive integer $n$, the small divisors of $n$ are defined as the positive divisors that do not exceed $\sqrt{n}.$ Ianucci previously classified all $n$ for which the small divisors of $n$ form an arithmetic progression. In this paper, we classify all $n$ for which the small divisors of $n$ form a linear recurrence of order at most two.

math.NT↗