Diophantine approximation with smooth numbers

Roger Baker

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arXiv · 2007.05823

Diophantine approximation with smooth numbers

Roger Baker

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Abstract

We prove a theorem about approximation to an irrational number by rational numbers whose denominator n is free of prime factors bigger than a power of log n. We strengthen the result in version 1 by using an exponential sum over smooth numbers tailored to the application. The new exponent approaches 1/3 as the exponent of log n becomes large.

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Roger Baker. 2020-07-11. Diophantine approximation with smooth numbers. https://arxiv.org/abs/2007.05823

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