Rational points on certain quintic hypersurfaces

DOI10.4064/AA138-4-5zbMATH Open1233.11035arXiv0810.0225OpenAlexW2006049243MaRDI QIDQ3184328

Maciej Ulas

Publication date: 14 October 2009

Published in: Acta Arithmetica (Search for Journal in Brave)

Abstract: Let $$ and consider the hypersurface of degree five given by the equation cal{V}_{f}: f(p)+f(q)=f(r)+f(s). Under the assumption $beq0$ we show that there exists $Q$-unirational elliptic surface contained in $cal{V}_f$. If $b=0,a<0$ and $-aotequiv2,18,34pmod48$ then there exists $Q$-rational surface contained in $cal{V}_f$. Moreover, we prove that for each $f$ of degree five there exists $Q(i)$-rational surface contained in $cal{V}_f$.

Full work available at URL: https://arxiv.org/abs/0810.0225

zbMATH Keywords

rational pointsdiophantine equationelliptic surfacequintic hypersurface

Mathematics Subject Classification ID

Rational points (14G05) Varieties over global fields (11G35) Diophantine equations in many variables (11D72) Higher degree equations; Fermat's equation (11D41)

Related Items (4)

Rational points on \(X_0^+(125)\) ⋮ Rational \(D(q)\)-quintuples ⋮ On the rationality of certain Weierstrass spaces of type \((5, g)\) ⋮ Unnamed Item

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