On monic abelian traceone cubic polynomials
Abstract
We compute the asymptotic number of monic traceone integral polynomials with Galois group $C_3$ and bounded height. For such polynomials we compute a height function coming from toric geometry and introduce a parametrization using the quadratic cyclotomic field $\mathbb Q(\sqrt{3})$. We also give a formula for the number of polynomials of the form $t^3 t^2 + at + b \in \mathbb Z[t]$ with Galois group $C_3$ for a fixed integer $a$.
 Publication:

arXiv eprints
 Pub Date:
 October 2023
 DOI:
 10.48550/arXiv.2310.17831
 arXiv:
 arXiv:2310.17831
 Bibcode:
 2023arXiv231017831B
 Keywords:

 Mathematics  Number Theory;
 11C08;
 11G50;
 14M25
 EPrint:
 24 pages