Year: 2025
Type: preprint
Abstract: Let $Y_1$ be a compact arithmetic hyperbolic surface associated to a maximal quaternion order, let $Y_q$ be a cover associated to an Eichler suborder of prime level $q$, and let $ι_q$ be embedding of $Y_q$ as the Hecke correspondence into $Y_1 \times Y_1$. Let $μ_1$ and $μ_q$ be the invariant probability measures on $Y_1$ and $Y_q$, respectively. If $F$ is a newform on $Y_q$, we conjecture that the pushforward measure $(ι_q)_\ast(\lvert F \rvert^2 μ_q)$ converges weakly to the uniform measure $μ_1 \times μ_1$, as $q$ tends to infinity. We prove this conjecture with an effective rate of equidistribution, assuming GRH.
Source: arXiv (Cornell University)
Authors: Nordentoft, Asbjørn Christian, Toma, Radu
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4416695381
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