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arXiv · 1701.06614

A congruence sum and rational approximations

Sandro Bettin
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Abstract

We give a reciprocity formula for a two-variable sum where the variables satisfy a linear congruence condition. We also prove that such sum is a measure of how well a rational is approximable from below and show that the reciprocity formula is a simple consequence of this fact.

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Sandro Bettin. 2017-01-23. A congruence sum and rational approximations. https://doi.org/10.1007/s12215-016-0288-0

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