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- W4289362941 abstract "For any $varepsilon > 0$ we derive effective estimates for the size of a non-zero integral point $m in mathbb{Z}^d setminus {0}$ solving the Diophantine inequality $lvert Q[m] rvert < varepsilon$, where $Q[m] = q_1 m_1^2 + ldots + q_d m_d^2$ denotes a non-singular indefinite diagonal quadratic form in $d geq 5$ variables. In order to prove our quantitative variant of the Oppenheim conjecture, we extend an approach developed by Birch and Davenport [BD58b] to higher dimensions combined with a theorem of Schlickewei [Sch85]. The result obtained is an optimal extension of Schlickewei's result, giving bounds on small zeros of integral quadratic forms depending on the signature $(r,s)$, to diagonal forms up to a negligible growth factor." @default.
- W4289362941 created "2022-08-02" @default.
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- W4289362941 date "2018-10-28" @default.
- W4289362941 modified "2023-09-27" @default.
- W4289362941 title "Small Values of Indefinite Diagonal Quadratic Forms at Integer Points in at least five Variables" @default.
- W4289362941 doi "https://doi.org/10.48550/arxiv.1810.11898" @default.
- W4289362941 hasPublicationYear "2018" @default.
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