Small representations of integers by integral quadratic forms

Wai Kiu Chan; Lenny Fukshansky

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arXiv · 1903.05123

Small representations of integers by integral quadratic forms

Wai Kiu Chan·Lenny Fukshansky

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Abstract

Given an isotropic quadratic form over a number field which assumes a value $t$, we investigate the distribution of points at which this value is assumed. Building on the previous work about the distribution of small-height zeros of quadratic forms, we produce bounds on height of points outside of some algebraic sets in a quadratic space at which the form assumes the value $t$. Our bounds on height are explicit in terms of the heights of the form, the space, the algebraic set and the value $t$.

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Wai Kiu Chan, Lenny Fukshansky. 2019-03-12. Small representations of integers by integral quadratic forms. https://arxiv.org/abs/1903.05123

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