arXiv subjects

Marios Voskou

Publications and source records attributed to Marios Voskou.

3 recordsLinked to original sources

arXiv2026

Refined Counting of Geodesic Segments in the Hyperbolic Plane

For $Γ$ a cofinite Fuchsian group, and $l$ a fixed closed geodesic, we study the asymptotics of the number of those images of $l$ that have a prescribed orientation and distance from $l$ less than or equal to $X$. Using a new relative trace formula that we develop, we give a new concrete proof of the error bound $O(X^{2/3})$ that appears in the works of Good and Hejhal. Furthermore, we prove a new bound $O(X^{1/2}\log{X})$ for the mean square of the error. For particular arithmetic groups, we provide interpretations in terms of correlation sums of the number of ideals of norm at most $X$ in associated number fields, generalizing previous examples due to Hejhal.

math.NT↗

arXiv2025

An $Ω$-Result for the Counting of Geodesic Segments in the Hyperbolic Plane

Let $Γ$ be a cocompact Fuchsian group, and $l$ a fixed closed geodesic. We study the counting of those images of $l$ that have a distance from $l$ less than or equal to $R$. We prove an $Ω$-result for the error term in the asymptotic expansion of the counting function. More specifically, we prove that the error term is equal to $Ω_δ\left(X^{1/2}\left(\log{\log{X}}\right)^{1/4-δ} \right)$, where $X=\cosh{R}$.

math.NT↗

arXiv2024

Large Sieve Inequalities for periods of Maass forms

For $Γ$ a Fuchsian Group of the first kind, we obtain large sieve inequalities with weights the hyperbolic periods of Maass forms of even weight. This is inspired by work of Chamizo, who proved a large sieve inequality with weights values of Maass forms of weight $0$. The motivation is applications in counting problems in $Γ_1 \backslash Γ/ Γ_2$, where $Γ_1$, $Γ_2$ are hyperbolic subgroups of $Γ$.

math.NT↗