This research reveals classical forms in biquadratic fields and derives bounds on binary quadratic forms, indicating notable differences from integers.
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.
No takes yet. Share an insight, caveat, or question.
Fryšová et al. (2025) studied this question.