{"id":"openai-math/Equidistribution-of-Primitive-Quartic-Torus-Packets-for-Arbitrary-Orders","pdf":"https://github.com/openai/math/blob/main/preprints/Equidistribution-of-Primitive-Quartic-Torus-Packets-for-Arbitrary-Orders-October-5-2026/quartic-torus-packets.pdf","url":"https://github.com/openai/math/tree/main/preprints/Equidistribution-of-Primitive-Quartic-Torus-Packets-for-Arbitrary-Orders-October-5-2026","tags":["number-theory","equidistribution","quartic-fields"],"score":0,"title":"Equidistribution of primitive quartic torus packets for arbitrary orders","domain":"Number theory","family":"015","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.NT","summary":"Let K range over totally real quartic fields with no proper intermediate field, and let $`\\mathcal O`$ be any order in K . We prove that the packets of periodic diagonal orbits attached to invertible $`\\mathcal O`$-ideal classes, weighted by orbit volume, equidistribute with no escape of mass as $`|\\mathop{\\mathrm{Disc}}\\nolimits (\\mathcal O)|`$ tends to infinity. The proof combines measure rigidity with a cubic-resolvent estimate that remains uniform at primes dividing the order index.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-10-05","reactions":{},"formalized":false,"family_title":"Torus-packet equidistribution in prime, quartic, and sextic degrees"}