The Hardy–Littlewood conjecture and rational points

DOI10.1112/S0010437X14007568zbMath1318.14024arXiv1304.3333OpenAlexW2148096752WikidataQ122956357 ScholiaQ122956357MaRDI QIDQ5173073

Olivier Wittenberg, Alexei N. Skorobogatov, Yonatan Harpaz

Publication date: 6 February 2015

Published in: Compositio Mathematica (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1304.3333

zbMATH Keywords

rational pointsweak approximationHasse principleBrauer-Manin obstructionfibration methodBunyakovski-Schinzel conjecture

Mathematics Subject Classification ID

Goldbach-type theorems; other additive questions involving primes (11P32) Rational points (14G05) Arithmetic ground fields (finite, local, global) and families or fibrations (14D10) Varieties over global fields (11G35) Global ground fields in algebraic geometry (14G25) Multiplicative and norm form equations (11D57)

Related Items (12)

On the equation N _{K /k} (Ξ)=P (t ) ⋮ Strong approximation and descent ⋮ Average Bateman–Horn for Kummer polynomials ⋮ SIEVES AND THE MINIMAL RAMIFICATION PROBLEM ⋮ Principes locaux-globaux pour certaines fibrations en torseurs sous un tore ⋮ Schinzel hypothesis on average and rational points ⋮ Arithmetic of del Pezzo surfaces of degree 4 and vertical Brauer groups ⋮ Integral points on conic log K3 surfaces ⋮ The value of polynomials represented by norm forms ⋮ On the fibration method for zero-cycles and rational points ⋮ Rational points on fibrations with few non-split fibres ⋮ Rational points and prime values of polynomials in moderately many variables

Cites Work

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• An inverse theorem for the Gowers \(U^{s+1}[N\)-norm]

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