Random Diophantine inequalities of additive type

Details Random Diophantine inequalities of additive type Random Diophantine inequalities of additive type

2011-10-16

arxiv.org/abs/1110.3496v1

Mathematics

Number Theory

13 pages

Scientific paper

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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