Let $p$ be a fixed prime number. Let $S_k(N)$ be the space of cusp forms of weight $k$ and level $N$. We prove a weighted equidistribution theorem for the eigenvalues of the $p$-th Hecke operator $T_p$ acting on $S_k(N)$. This is a variant of a celebrated theorem of Serre.
Publié le : 2008-12-15
Classification:
Eigenvalues of Hecke operators,
equidistribution,
summation methods,
Petersson trace formula,
11F25,
11F30
@article{1229696570,
author = {Gun, Sanoli and Murty, M. Ram and Rath, Purusottam},
title = {Summation methods and distribution of eigenvalues of Hecke operators},
journal = {Funct. Approx. Comment. Math.},
volume = {38},
number = {1},
year = {2008},
pages = { 191-204},
language = {en},
url = {http://dml.mathdoc.fr/item/1229696570}
}
Gun, Sanoli; Murty, M. Ram; Rath, Purusottam. Summation methods and distribution of eigenvalues of Hecke operators. Funct. Approx. Comment. Math., Tome 38 (2008) no. 1, pp. 191-204. http://gdmltest.u-ga.fr/item/1229696570/