We explore numerically the eigenvalues of the hermitian form
when . We improve on the existing upper bound, and produce a (conjectural) plot of the asymptotic distribution of its eigenvalues by exploiting fairly extensive computations. The main outcome is that this asymptotic density most probably exists but is not continuous with respect to the Lebesgue measure.
Nous explorons numériquement les valeurs de la forme hermitienne
lorsque . Nous améliorons la majoration actuelle et exhibons un graphique conjectural de la distribution asymptotique de ses valeurs propres en exploitant des résultats de calculs intensifs. L’une des conséquences est que la distribution asymptotique existe probablement mais n’est pas absolument continue par rapport à la mesure de Lebesgue.
Keywords: Large sieve inequality, circle method, Jackson polynomials, Hausdorff moment problem
Olivier Ramaré 1
@article{JTNB_2010__22_1_181_0, author = {Olivier Ramar\'e}, title = {Eigenvalues in the large sieve inequality, {II}}, journal = {Journal de th\'eorie des nombres de Bordeaux}, pages = {181--196}, publisher = {Universit\'e Bordeaux 1}, volume = {22}, number = {1}, year = {2010}, doi = {10.5802/jtnb.710}, mrnumber = {2675879}, zbl = {1220.11117}, language = {en}, url = {https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.710/} }
TY - JOUR AU - Olivier Ramaré TI - Eigenvalues in the large sieve inequality, II JO - Journal de théorie des nombres de Bordeaux PY - 2010 SP - 181 EP - 196 VL - 22 IS - 1 PB - Université Bordeaux 1 UR - https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.710/ DO - 10.5802/jtnb.710 LA - en ID - JTNB_2010__22_1_181_0 ER -
%0 Journal Article %A Olivier Ramaré %T Eigenvalues in the large sieve inequality, II %J Journal de théorie des nombres de Bordeaux %D 2010 %P 181-196 %V 22 %N 1 %I Université Bordeaux 1 %U https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.710/ %R 10.5802/jtnb.710 %G en %F JTNB_2010__22_1_181_0
Olivier Ramaré. Eigenvalues in the large sieve inequality, II. Journal de théorie des nombres de Bordeaux, Volume 22 (2010) no. 1, pp. 181-196. doi : 10.5802/jtnb.710. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.710/
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