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Corpus ID: 248863451

Some new results in quantitative Diophantine approximation

@inproceedings{Ghosh2021SomeNR,
title={Some new results in quantitative Diophantine approximation},
author={Anish Ghosh and V. Vinay Kumaraswamy},
year={2021}
}

. In this article we establish two new results on quantitative Diophantine approximation for one-parameter families of diagonal ternary indeﬁnite forms. In the ﬁrst result, we consider quadratic forms taking values at prime points. In the second, we examine inhomogeneous forms of arbitrary degree taking values at integer points.

Let $k\geq 2$ and consider the Diophantine inequality $$ \left|x_1^k-{\alpha}_2 x_2^k-{\alpha}_3 x_3^k\right| <{\theta}.$$Our goal is to find non-trivial solutions in the variables $x_i$, $1\leq… Expand

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