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Preprint in the OpenAI Math release

Equidistribution of primitive quartic torus packets for arbitrary orders

OpenAI

Abstract

Let K range over totally real quartic fields with no proper intermediate field, and let be any order in K. We prove that the packets of periodic diagonal orbits attached to invertible -ideal classes, weighted by orbit volume, equidistribute with no escape of mass as tends to infinity. The proof combines measure rigidity with a cubic-resolvent estimate that remains uniform at primes dividing the order index.

open until 1 Jan 2028

est. 50% chance this result is independently verified by the end of 2027.

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