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arXiv · 1110.3496

Random Diophantine inequalities of additive type

Jörg Brüdern·Rainer Dietmann
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Abstract

Using the Davenport-Heilbronn circle method, we show that for almost all additive Diophantine inequalities of degree $k$ in more than $2k$ variables the expected asymptotic formula for the density of solutions holds true. This appears to be the first metric result on Diophantine inequalities.

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Jörg Brüdern, Rainer Dietmann. 2011-10-16. Random Diophantine inequalities of additive type. https://arxiv.org/abs/1110.3496

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