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arXiv · 2605.29470

The weighted large sieve through Parseval

Olivier Ramaré
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Abstract

We modify the approach to the arithmetical form of the large sieve by relying on the Parseval identity rather than on an approximate Bessel inequality and as a consequence, improve on the weighted large sieve inequality beyond what was heuristically accessible by the earlier approach. We also discuss the optimality of this approach.

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Olivier Ramaré. 2026-05-28. The weighted large sieve through Parseval. https://arxiv.org/abs/2605.29470

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