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arXiv · 2509.23857

Additively indecomposable quadratic forms over biquadratic and simplest cubic fields

Simona Fryšová·Magdaléna Tinková
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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.

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Simona Fryšová, Magdaléna Tinková. 2025-09-28. Additively indecomposable quadratic forms over biquadratic and simplest cubic fields. https://arxiv.org/abs/2509.23857

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