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arXiv · 2601.18581

The Hasse principle for diagonal forms restricted to a hypersurface of adjacent degree

Anna Theorin Johansson
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Abstract

We investigate the Hasse principle for Diophantine systems consisting of one diagonal form of degree $k$ and one general form of degree $k-1$. By refining the method of Brandes and Parsell (arXiv:2003.04350) in this specific setting, we improve the bound $n > 2^k k$ to $n > 2^{k-1}(2k-1)$; in particular, the requirement $n > 24$ in the case of degrees three and two is relaxed to $n > 20$.

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Anna Theorin Johansson. 2026-01-26. The Hasse principle for diagonal forms restricted to a hypersurface of adjacent degree. https://arxiv.org/abs/2601.18581

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