Joint equidistribution of newforms

Asbjørn Christian Nordentoft; Radu Toma

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arXiv · 2509.01602

Joint equidistribution of newforms

Asbjørn Christian Nordentoft·Radu Toma

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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.

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BibTeX RIS

Asbjørn Christian Nordentoft, Radu Toma. 2025-09-01. Joint equidistribution of newforms. https://arxiv.org/abs/2509.01602

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