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arXiv · 2610.35639

On the Hasse principle for a block-diagonal form and a form of lower degree

Anna Theorin Johansson
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Abstract

We investigate the Hasse principle for systems consisting of one form of degree $k$ which decomposes as a sum of $n$-ary forms, and one general form of degree $d < k$. By exploiting the block structure of the first form before applying Weyl differencing, we refine the method of Brandes and Parsell (arXiv:2003.04350) in this setting; in particular, for a sum of binary quartic forms and a quadratic form, the requirement $s > 516$ is relaxed to $s > 96$, which also improves on the bound $s > 100$ available for general forms.

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Anna Theorin Johansson. 2026-10-26. On the Hasse principle for a block-diagonal form and a form of lower degree. https://arxiv.org/abs/2610.35639

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