Let d₃ ≥ p₂ > p₁ ≥ 3 be integers such that p₁,p₂ are prime numbers. We show that the sequence (p₁,p₂,d₃) is the multidegree of some tame automorphism of ℂ³ if and only if d₃ ∈ p₁ℕ + p₂ℕ, i.e. if and only if d₃ is a linear combination of p₁ and p₂ with coefficients in ℕ.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ba59-1-4,
author = {Marek Kara\'s},
title = {Tame Automorphisms of C3 with Multidegree of the Form (p1,p2,d3)},
journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
volume = {59},
year = {2011},
pages = {27-32},
zbl = {1215.14059},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba59-1-4}
}
Marek Karaś. Tame Automorphisms of ℂ³ with Multidegree of the Form (p₁,p₂,d₃). Bulletin of the Polish Academy of Sciences. Mathematics, Tome 59 (2011) pp. 27-32. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba59-1-4/