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.
Publié le : 2007-09-15
Classification:
large sieve inequality,
circle method,
11L03,
11L07,
11L26,
11N35
@article{1229619662,
author = {Ramar\'e, Olivier},
title = {Eigenvalues in the large sieve inequality},
journal = {Funct. Approx. Comment. Math.},
volume = {37},
number = {1},
year = {2007},
pages = { 399-427},
language = {en},
url = {http://dml.mathdoc.fr/item/1229619662}
}
Ramaré, Olivier. Eigenvalues in the large sieve inequality. Funct. Approx. Comment. Math., Tome 37 (2007) no. 1, pp. 399-427. http://gdmltest.u-ga.fr/item/1229619662/