Functiones et Approximatio Commentarii Mathematici

Eigenvalues in the large sieve inequality

Olivier Ramaré

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We provide some evidence that the eigenvalues of the hermitian form $\sum_{a/q}|\sum_{n\le N}\varphi_ne(na/q)|^2$ tend to have a limit distribution when $N$ and $Q$ go simultaneously to infinity in such a way that $N/Q^2$ tends to a constant. We also present some background material, as well as a large sieve equality, when $N\Log^7 N = o(Q)$, that follows from our results.

Article information

Funct. Approx. Comment. Math., Volume 37, Number 2 (2007), 399-427.

First available in Project Euclid: 18 December 2008

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 11L03: Trigonometric and exponential sums, general 11L07: Estimates on exponential sums 11L26: Sums over arbitrary intervals
Secondary: 11N35: Sieves

large sieve inequality circle method


Ramaré, Olivier. Eigenvalues in the large sieve inequality. Funct. Approx. Comment. Math. 37 (2007), no. 2, 399--427. doi:10.7169/facm/1229619662.

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