Cubic hypersurfaces and a version of the circle method for number fields

Tim Browning; Pankaj Vishe

doi:10.1215/00127094-2738530

Cubic hypersurfaces and a version of the circle method for number fields

Tim Browning, Pankaj Vishe

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

A version of the Hardy-Littlewood circle method is developed for number fields K/Q and is used to show that non-singular projective cubic hypersurfaces over K always have a K-rational point when they have dimension at least 8.

Original language	English
Pages (from-to)	1825-1883
Journal	Duke Mathematical Journal
Volume	163
Issue number	10
DOIs	https://doi.org/10.1215/00127094-2738530
Publication status	Published - 2014

Bibliographical note

47 pages; numerous minor changes. (c) 2014. This is an author produced version of a paper accepted for publication in Duke Mathematical Journal. Uploaded in accordance with the publisher's self-archiving policy.

Keywords

math.NT
11P55 (Primary) 11D72, 14G05 (Secondary)

Access to Document

10.1215/00127094-2738530

12072385v2
(c) 2014. This is an author produced version of a paper accepted for publication in Duke Mathematical Journal. Uploaded in accordance with the publisher's self-archiving policy.
Submitted manuscript, 397 KB

Programme Grant-New Frameworks in metric Number Theory
Velani, S. (Principal investigator) & Beresnevich, V. (Other)
EPSRC
1/06/12 → 30/11/18
Project: Research project (funded) › Research

Cite this

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title = "Cubic hypersurfaces and a version of the circle method for number fields",

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KW - 11P55 (Primary) 11D72, 14G05 (Secondary)

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Cubic hypersurfaces and a version of the circle method for number fields

Abstract

Bibliographical note

Keywords

Access to Document

Projects

Programme Grant-New Frameworks in metric Number Theory

Cite this