English

Simultaneous additive equations: Repeated and differing degrees

Number Theory 2019-08-15 v1

Abstract

We obtain bounds for the number of variables required to establish Hasse principles, both for existence of solutions and for asymptotic formulae, 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.

Keywords

Cite

@article{arxiv.1508.03169,
  title  = {Simultaneous additive equations: Repeated and differing degrees},
  author = {Julia Brandes and Scott T. Parsell},
  journal= {arXiv preprint arXiv:1508.03169},
  year   = {2019}
}
R2 v1 2026-06-22T10:32:50.036Z