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arXiv · 1004.5527

Random diophantine equations of additive type

Jörg Brüdern·Rainer Dietmann
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Abstract

Using the circle method in combination with lattice point counting arguments, we show that for almost all homogeneous diophantine equations of additive type and degree $k$ in more than $4k$ variables, the Local-Global principle holds true. Moreover, our approach shows that almost all such equations having a non-trivial integer solution have a very small such solution, the bound being close to the best possible one.

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Jörg Brüdern, Rainer Dietmann. 2010-04-30. Random diophantine equations of additive type. https://arxiv.org/abs/1004.5527

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