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arXiv · 1202.5026

Forms representing forms and linear spaces on hypersurfaces

Julia Brandes
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Abstract

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.

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Julia Brandes. 2013-07-26. Forms representing forms and linear spaces on hypersurfaces. https://doi.org/10.1112/plms%2Fpdt045

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