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arXiv:1202.5026 [math.NT]AbstractReferencesReviewsResources

Forms representing forms and linear spaces on hypersurfaces

Julia Brandes

Published 2012-02-22, updated 2013-07-26Version 3

A generalisation of Waring's problem, considered first by Arkhipov and Karatsuba, is the question of representing not an integer, but a given polynomial, as a sum of powers of linear polynomials. We investigate a related problem and prove a Hasse principle for the number of identical representations of a set of given forms by homogeneous polynomials of general shape. The result leads to sizeable improvements for estimates of the number of linear spaces on the intersection of hypersurfaces.

Comments: 26 pages; v.2: the main part of the argument has been expanded and an error has been fixed, v.3: various typos have been corrected. Accepted for publication at the Proceedings of the LMS
Categories: math.NT
Subjects: 11D72, 11E76, 11P55
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