Random diophantine equations, I
Number Theory
2012-12-20 v1
Abstract
We consider additive diophantine equations of degree in variables and establish that whenever then almost all such equations satisfy the Hasse principle. The equations that are soluble form a set of positive density, and among the soluble ones almost all equations admit a small solution. Our bound for the smallest solution is nearly best possible.
Cite
@article{arxiv.1212.4800,
title = {Random diophantine equations, I},
author = {Jörg Brüdern and Rainer Dietmann},
journal= {arXiv preprint arXiv:1212.4800},
year = {2012}
}
Comments
The results in this paper use an $L^2$-technique and supersede those in an earlier version (see arXiv:1110.3496) that relied on an $L^1$-argument, but for instructional purposes we found it useful to keep the older, technically simpler version. arXiv admin note: substantial text overlap with arXiv:1004.5527