Forms representing forms and linear spaces on hypersurfaces

Details Forms representing forms and linear spaces on hypersurfaces Forms representing forms and linear spaces on hypersurfaces

2012-02-22

arxiv.org/abs/1202.5026v1

Mathematics

Number Theory

23 pages

Scientific paper

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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