The Dixmier conjecture and the shape of possible counterexamples

Abstract

We establish a lower bound for the size of possible counterexamples of the Dixmier Conjecture. We prove that $B>15$, where $B$ is the minimum of the greatest common divisor of the total degrees of $P$ and $Q$, where $(P,Q)$ runs over the counterexamples of the Dixmier Conjecture.

arXiv comment43 pages; 6 figures; this a resume version made out of the previous version and "The Dixmier conjecture and the shape of possible counterexamples II"