Quartic Forms in Many Variables

Abstract

We show that a quartic $p$-adic form with at least $3192$ variables possesses a non-trivial zero. We also prove new results on systems of cubic, quadratic and linear forms. As an example, we show that for a system comprising two cubic forms $132$ variables are sufficient.

8 pages

Cited by in corpus (1)

• A note on p-adic solubility for forms in many variables