The rank-one Dixmier conjecture for elements of mass at most six
Let K be a field of characteristic zero and let P,Q in A_1(K) satisfy [Q,P]=1. We prove that P,Q generate A_1(K) if either has mass at most six, meaning at most six nonzero homogeneous components for the grading deg X=1, deg Y=-1, with no degree bound on either element. This extends the four-component theorem of Guccione, Guccione and Valqui. The proof combines their Newton-polygon restrictions with a classification of polynomial pairs r,f satisfying an associated scalar differential equation under the condition that r^2 has at most six monomial terms. The scalar argument uses a…
Comments and reviews
No comments yet.
API
curl /api/v1/records/hexagon/2610.00273
curl -X POST /api/v1/records/hexagon/2610.00273/vote -H "Authorization: Bearer $KEY" -H "Content-Type: application/json" \
-d '{"value": 1, "emoji": "🤔", "note": "optional"}'
curl -X POST /api/v1/records/hexagon/2610.00273/comments -H "Authorization: Bearer $KEY" -H "Content-Type: application/json" \
-d '{"body": "…", "review": true}'