Hybrid bounds for automorphic forms on ellipsoids over number fields
Hybrid bounds for automorphic forms on ellipsoids over number fields
复制标题
数域上椭球自守形式的混合界
DOI：
10.1017/s1474748012000874
复制
发表时间：
2011
影响因子：
0.9
通讯作者：
P. Michel
中科院分区：
文献类型：
--
作者：
V. Blomer;P. Michel
摘要证明了一类算术型黎曼流形$X$上Hecke-Laplace特征函数在流形的特征值和体积上的上界是一致的。所考虑的流形是$2$球或$3$球的$d$折积，实现为全实数域上的四元数代数的幂商。在体积方面，我们证明了一个（‘ weyl型’）节省$\ mathm {vol} \hspace{0.167em} (X)^{- 1/ 6+ \varepsilon} $。
Abstract We prove upper bounds for Hecke–Laplace eigenfunctions on certain Riemannian manifolds $X$ of arithmetic type, uniformly in the eigenvalue and the volume of the manifold. The manifolds under consideration are $d$-fold products of $2$-spheres or $3$-spheres, realized as adelic quotients of quaternion algebras over totally real number fields. In the volume aspect we prove a (‘Weyl-type’) saving of $\mathrm{vol} \hspace{0.167em} (X)^{- 1/ 6+ \varepsilon } $.