Additively indecomposable quadratic forms over biquadratic and simplest cubic fields
Number Theory
2026-02-10 v2
Abstract
In this paper, we study additively indecomposable quadratic forms over real biquadratic and simplest cubic fields. In particular, we show that over these fields, we can always find such a classical form in 2 variables, which differs from the situation for forms over integers. Moreover, for some cases, we derive a lower bound on the number of classical, additively indecomposable binary quadratic forms up to equivalence.
Cite
@article{arxiv.2509.23857,
title = {Additively indecomposable quadratic forms over biquadratic and simplest cubic fields},
author = {Simona Fryšová and Magdaléna Tinková},
journal= {arXiv preprint arXiv:2509.23857},
year = {2026}
}