Solvability of systems of diagonal equations over p‐adic local fields

Abstract

We prove that a system of R diagonal equations of degree d over a finite extension K of Qp has a non‐trivial solution in K if the number of variables exceeds 3R2d2 (if p>2) or 8R2d2 (if p=2). As a consequence, a system of R homogeneous equations of degree d over K has a non‐trivial solution in K if the number of variables exceeds false(8R2d2false)2d−1.