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4. Equidistribution of CM points

Problems from the afternoon session of January 29, 2024

    1. Joint equidistribution of CM points


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      Problem 4.1.

      [Chris Skinner] Determine the joint equidistribution of CM points over $K$ of products of modular curves over $F$ as $\mathrm{disc}(K) \rightarrow \infty$.

        • Arithmetic applications of horizontal equidistribution results


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          Problem 4.2.

          [Philippe Michel] Let $K$ be an imaginary quadratic number fields. There are equidistribution results for CM points with square-free order of conductor $C$ as $C \rightarrow \infty$.

          Is there an interesting arithmetic application for this?
              Note: we can ask the same question for similar results in broader contexts.

              Cite this as: AimPL: Analytic, arithmetic, and geometric aspects of automorphic forms, available at http://aimpl.org/aagaautomorphic.