# Small Values of Indefinite Diagonal Quadratic Forms at Integer Points in at least five Variables

@article{Buterus2018SmallVO, title={Small Values of Indefinite Diagonal Quadratic Forms at Integer Points in at least five Variables}, author={Paul Buterus and Friedrich Gotze and Thomas Hille}, journal={arXiv: Number Theory}, year={2018} }

For any $\epsilon >0$ we derive an effective estimate for a solution of $|Q[m]| < \epsilon$ in non-zero integral points $m \in \mathbb Z^d \setminus \{0\}$ in terms of the signature $(r,s)$ and the largest eigenvalue, where $Q[x] = \sum_{i=1}^d \lambda_i x_i^2$ is a non-singular indefinite diagonal quadratic form of dimension $d \geq 5$. In order to prove our result, we extend an approach of Birch and Davenport(1958b) to higher dimensions combined with a theorem of Schlickewei (1985) on small… Expand

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