Michel–Venkatesh mixing conjecture for shifted Heegner packets

From papers

Let d\ftyd\to\fty along D{\mathbb D}^\flat, let RdΔ([s]){\sf R}_d^\Delta([\mathfrak s]) be the shifted diagonal Heegner packet, let μ\mu be the quotient measure on S2{\sf S}^2, and let qq be the smallest norm of an integral ideal representing the class [s][\mathfrak s]. Michel–Venkatesh mixing conjecture. The set

d1/2RdΔ([s])d^{-1/2}{\sf R}_d^\Delta([\mathfrak s])

equidistributes relative to the product measure μ×μ\mu\times\mu on S2×S2{\sf S}^2\times{\sf S}^2 provided that qq\to\infty as dd\to\infty along D{\mathbb D}^\flat. This is a disjointness or mixing statement for class-group self-joinings of Heegner packets, strengthening ordinary equidistribution by requiring the shifted pairs to become independent in the limit.

Progress summary

Nothing recorded yet. Refresh searches the literature and the public web for attempts on this problem, and writes the first summary here.

Sources & referencesView supporting material

Primary source

Valentin Blomer, Farrell Brumley and Ilya Khayutin, “The mixing conjecture under GRH”, arXiv:2212.06280 (2025).

Solutions 0

No solutions have been posted yet.