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

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JournalDuke Mathematical Journal
DatePublished - 2014
Issue number10
Volume163
Pages (from-to)1825-1883
Original languageEnglish

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.

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.

    Research areas

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

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