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arXiv · 1212.4800

Random diophantine equations, I

Jörg Brüdern·Rainer Dietmann
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Abstract

We consider additive diophantine equations of degree $k$ in $s$ variables and establish that whenever $s\ge 3k+2$ 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.

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Jörg Brüdern, Rainer Dietmann. 2012-12-19. Random diophantine equations, I. https://arxiv.org/abs/1212.4800

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