Author:
Brandes Julia,Parsell Scott T.
Abstract
Abstract
We obtain bounds for the number of variables required to establish Hasse
principles, both for the existence of solutions and for asymptotic formulæ, for
systems of additive equations containing forms of differing degree but also
multiple forms of like degree. Apart from the very general estimates of Schmidt
and Browning–Heath–Brown, which give weak results when specialized to the diagonal
situation, this is the first result on such “hybrid” systems. We also obtain
specialized results for systems of quadratic and cubic forms, where we are able to
take advantage of some of the stronger methods available in that setting. In
particular, we achieve essentially square root cancellation for systems consisting
of one cubic and r quadratic equations.
Publisher
Canadian Mathematical Society
Cited by
3 articles.
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