Corpus ID: 119617623

# 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}
}
• Published 28 October 2018
• Mathematics
• arXiv: Number Theory
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
1 Citations
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