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arXiv · 1801.03735

Diophantine inequalities for generic ternary diagonal forms

Damaris Schindler
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Abstract

Let k\geq 2 and consider the Diophantine inequality |x_1^k-\alp_2 x_2^k-\alp_3 x_3^k| <\tet. Our goal is to find non-trivial solutions in the variables x_i, 1\leq i\leq 3, all of size about P, assuming that \tet is sufficiently large. We study this problem on average over \alp_3 and generalize previous work of Bourgain on quadratic ternary diagonal forms to general degree k.

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Damaris Schindler. 2018-01-11. Diophantine inequalities for generic ternary diagonal forms. https://arxiv.org/abs/1801.03735

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