We prove an effective version of a result due to Einsiedler, Mozes, Shah and Shapira on the
asymptotic distribution of primitive rational points on expanding closed horospheres in the …

We establish higher dimensional versions of a recent theorem by Chen and Haynes [Int. J.
Number Theory 19 (2023), 1405–1413] on the expected value of the smallest denominator …

Linnik proved in the late 1950's the equidistribution of integer points on large spheres under
a congruence condition. The congruence condition was lifted in 1988 by Duke (building on a …

We count primitive lattices of rank d inside as their covolume tends to infinity, with respect to
certain parameters of such lattices. These parameters include, for example, the subspace …

The set of primitive vectors on large spheres in the euclidean space of dimension
equidistribute when projected on the unit sphere. We consider here a refinement of this …

Distribution of shapes of orthogonal lattices Page 1 Ergod. Th. & Dynam. Sys. (2019), 39,
1531–1607 doi:10.1017/etds.2017.78 c Cambridge University Press, 2017 Distribution of …

Let $\nu $ be a place of a global function field $ K $ over a finite field, with associated affine
function ring $ R_\nu $ and completion $ K_\nu $, and let $1\leq\mathfrak {m}<\textbf {d} …

Matrix Kloosterman sums Page 1 Algebra & Number Theory msp Volume 18 2024 No. 12
Matrix Kloosterman sums Márton Erdélyi and Árpád Tóth Page 2 msp ALGEBRA AND …

Let $\theta\in\mathbb {R}^ d $. We associate three objects to each approximation $(p,
q)\in\mathbb {Z}^ d\times\mathbb {N} $ of $\theta $: the projection of the lattice $\mathbb …

We construct a perverse sheaf related to the the matrix exponential sums investigated by
Erdélyi and Tóth [Matrix Kloosterman sums, 2021, arXiv: 2109.00762]. As this sheaf appears …