Dimitrios Chatzakos

activity

20152026

collaborators

12 papers

math.NT2026

Pointwise improvement of the error term in the higher rank hyperbolic lattice counting problem

Dimitrios Chatzakos, Panagiotis Dimakis, Christos Katsivelos

We prove an upper bound for the error term in the higher rank hyperbolic lattice counting problem for $SL (n, Z)$ . Blomer and Lutsko achieved recently a significan…

math.NT2026

Square root cancellation in the hyperbolic lattice counting problem over cocompact groups

Dimitrios Chatzakos, Panagiotis Dimakis

For cocompact Fuchsian groups $Γ \leq PSL (2, R)$ we improve Selberg's bound for the error term of the counting function in the hyperbolic lattice counting problem, a…

math.NT2026

Square-root cancellation for sums of coefficients of $GL (m)$ -automorphic forms over values of random polynomials

Dimitrios Chatzakos, Efthymios Sofos

For arbitrary $m \geq 2$ and $d \geq 1$ , we establish square-root cancellation for sums of Fourier coefficients of $GL (m)$ -automorphic forms averaged over values of random d…

math.NT2025

The hyperbolic circle problem over Heegner points

Dimitrios Chatzakos, Giacomo Cherubini, Stephen Lester +1

For the full modular group, we obtain a logarithmic improvement on Selberg's long-standing bound for the error term of the counting function in the hyperbolic circle problem over H…

math.NT2020

On the distribution of lattice points on hyperbolic circles

Dimitrios Chatzakos, Par Kurlberg, Stephen Lester +1

We study the fine distribution of lattice points lying on expanding circles in the hyperbolic plane $H$ . The angles of lattice points arising from the orbit of the modular…

math.NT2020

Quantum ergodicity for shrinking balls in arithmetic hyperbolic manifolds

Dimitrios Chatzakos, Robin Frot, Nicole Raulf

We study a refinement of the quantum unique ergodicity conjecture for shrinking balls on arithmetic hyperbolic manifolds, with a focus on dimensions $2$ and $3$ . For the Eisens…

math.NT2018

Second Moment of the Prime Geodesic Theorem for $PSL (2, Z [i])$

Dimitrios Chatzakos, Giacomo Cherubini, Niko Laaksonen

The remainder $E_{Γ} (X)$ in the Prime Geodesic Theorem for the Picard group $Γ = PSL (2, Z [i])$ is known to be bounded by $O (X^{3/2 + ε})$ under the assumption of the Li…

math.NT2018

CM-points and Lattice counting on arithmetic compact Riemann surfaces

Montserrat Alsina, Dimitrios Chatzakos

Let $X (D, 1) = Γ (D, 1) \ H$ denote the Shimura curve of level $N = 1$ arising from an indefinite quaternion algebra of fixed discriminant $D$ . We study the discrete av…

math.NT2017

Prime Geodesic Theorem in the 3-dimensional Hyperbolic Space

Olga Balkanova, Dimitrios Chatzakos, Giacomo Cherubini +2

For $Γ$ a cofinite Kleinian group acting on $H^{3}$ , we study the Prime Geodesic Theorem on $M = Γ\ H^{3}$ , which asks about the asymptotic behaviour of length…

math.NT2016

Mean value results and $Ω$ -results for the hyperbolic lattice point problem in conjugacy classes

Dimitrios Chatzakos

For $Γ$ a Fuchsian group of finite covolume, we study the lattice point problem in conjugacy classes on the Riemann surface $Γ\ H$ . Let $H$ be a hyperbo…

math.NT2015

$Ω$ -results for the hyperbolic lattice point problem

Dimitrios Chatzakos

For $Γ$ a cocompact or cofinite Fuchsian group, we study the lattice point problem on the Riemann surface $Γ\ H$ . The main asymptotic for the counting of the orbit…

math.NT2015

The hyperbolic lattice point problem in conjugacy classes

Dimitrios Chatzakos, Yiannis Petridis

For $Γ$ a cocompact or cofinite Fuchsian group, we study the hyperbolic lattice point problem in conjugacy classes, which is a modification of the classical hyperbolic lattice poin…

Pointwise improvement of the error term in the higher rank hyperbolic lattice counting problem

Square root cancellation in the hyperbolic lattice counting problem over cocompact groups

Square-root cancellation for sums of coefficients of GL(m)-automorphic forms over values of random polynomials

The hyperbolic circle problem over Heegner points

On the distribution of lattice points on hyperbolic circles

Quantum ergodicity for shrinking balls in arithmetic hyperbolic manifolds

Second Moment of the Prime Geodesic Theorem for PSL(2,Z[i])

CM-points and Lattice counting on arithmetic compact Riemann surfaces

Prime Geodesic Theorem in the 3-dimensional Hyperbolic Space

Mean value results and Ω-results for the hyperbolic lattice point problem in conjugacy classes

Ω-results for the hyperbolic lattice point problem

The hyperbolic lattice point problem in conjugacy classes

Square-root cancellation for sums of coefficients of $GL (m)$ -automorphic forms over values of random polynomials

Second Moment of the Prime Geodesic Theorem for $PSL (2, Z [i])$

Mean value results and $Ω$ -results for the hyperbolic lattice point problem in conjugacy classes

$Ω$ -results for the hyperbolic lattice point problem