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arXiv · 1512.03648

On two conjectures concerning squarefree numbers in arithmetic progressions

Ramon M. Nunes
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Abstract

We prove upper bounds for the error term of the distribution of squarefree numbers up to $X$ in arithmetic progressions modulo $q$ making progress towards two well-known conjectures concerning this distribution and improving upon earlier results by Hooley. We make use of recent estimates for short exponential sums by Bourgain-Garaev and for exponential sums twisted by the Möbius function by Bourgain and Fouvry-Kowalski-Michel.

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Ramon M. Nunes. 2015-12-11. On two conjectures concerning squarefree numbers in arithmetic progressions. https://arxiv.org/abs/1512.03648

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