Forms representing forms and linear spaces on hypersurfaces
Number Theory
2014-02-26 v3
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.
Keywords
Cite
@article{arxiv.1202.5026,
title = {Forms representing forms and linear spaces on hypersurfaces},
author = {Julia Brandes},
journal= {arXiv preprint arXiv:1202.5026},
year = {2014}
}
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