We give a reciprocity formula for a two-variables 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.
A congruence sum and rational approximations
Bettin, Sandro
2017-01-01
Abstract
We give a reciprocity formula for a two-variables 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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