On Pairs of Diagonal Quintic Forms |
| |
Authors: | Scott T Parsell Trevor D Wooley |
| |
Institution: | (1) Department of Mathematics, Texas A&M University, College Station, TX, 77843-3368, U.S.A.;(2) Department of Mathematics, University of Michigan, East Hall, 525 East University Avenue, Ann Arbor, MI, 48109-1109, U.S.A. |
| |
Abstract: | We demonstrate that a pair of additive quintic equations in at least 34 variables has a nontrivial integral solution, subject only to an 11-adic solubility hypothesis. This is achieved by an application of the Hardy–Littlewood method, for which we require a sharp estimate for a 33.998th moment of quintic exponential sums. We are able to employ p-adic iteration in a form that allows the estimation of such a mean value over a complete unit square, thereby providing an approach that is technically simpler than those of previous workers and flexible enough to be applied to related problems. |
| |
Keywords: | diophantine equations quintic forms the Hardy– Littlewood method |
本文献已被 SpringerLink 等数据库收录! |
|