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SHORTEST DISTANCE IN MODULAR HYPERBOLA AND LEAST QUADRATIC NON-RESIDUE
Published online by Cambridge University Press: 10 May 2016
Abstract
In this paper, we study how small a box contains at least two points from a modular hyperbola $xy\equiv c\;(\text{mod}\;p)$. There are two such points in a square of side length $p^{1/4+\unicode[STIX]{x1D716}}$. Furthermore, it turns out that either there are two such points in a square of side length $p^{1/6+\unicode[STIX]{x1D716}}$ or the least quadratic non-residue is less than $p^{1/(6\sqrt{e})+\unicode[STIX]{x1D716}}$.
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- Copyright © University College London 2016
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