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arXiv · 2609.25885

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. We compute in passing the $L^2$-norm of the Beurling-Selberg majorant of the characteristic function of an interval.

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Olivier Ramaré. 2026-09-22. The weighted large sieve through Parseval. https://arxiv.org/abs/2609.25885

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