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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 typeand degree $k$ in more than $4k$ variables, the Local-Global principle holdstrue. Moreover, our approach shows that almost all such equations having anon-trivial integer solution have a very small such solution, the bound beingclose to the best possible one.



Autor: Jörg Brüdern, Rainer Dietmann

Fuente: https://arxiv.org/



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