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arXiv · 1611.08312

Major arcs and moments of arithmetical sequences

Régis de la Bretèche·Daniel Fiorilli
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Abstract

We give estimates for the first two moments of arithmetical sequences in progressions. Instead of using the standard approximation, we work with a generalization of Vaughan's major arcs approximation which is similar to that appearing in earlier work of Browning and Heath-Brown on norm forms. We apply our results to the sequence $\tau_k(n)$, and obtain unconditional results in a wide range of moduli.

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Régis de la Bretèche, Daniel Fiorilli. 2016-11-24. Major arcs and moments of arithmetical sequences. https://arxiv.org/abs/1611.08312

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