Abstract
AbstractLet $$\theta $$
θ
be an elementary theta function, such as the classical Jacobi theta function. We establish a spectral decomposition and surprisingly strong asymptotic formulas for $$\langle |\theta |^2, \varphi \rangle $$
⟨
|
θ
|
2
,
φ
⟩
as $$\varphi $$
φ
traverses a sequence of Hecke-translates of a nice enough fixed function. The subtlety is that typically $$|\theta |^2 \notin L^2$$
|
θ
|
2
∉
L
2
. Applications to the subconvexity, quantum variance and 4-norm problems are indicated.
Funder
Swiss Federal Institute of Technology Zurich
Publisher
Springer Science and Business Media LLC
Reference36 articles.
1. Bernstein, J., Reznikov, A.: Sobolev norms of automorphic functionals. Int. Math. Res. Not. 40, 2155–2174 (2002)
2. Borel, A.: Introduction aux groupes arithmétiques. Publications de l’Institut de Mathématique de l’Université de Strasbourg, XV. Actualités Scientifiques et Industrielles, No. 1341. Hermann, Paris (1969)
3. Bump, D.: Automorphic Forms and Representations. Cambridge Studies in Advanced Mathematics, vol. 55. Cambridge University Press, Cambridge (1997)
4. Gan, W.T., Qiu, Y., Takeda, S.: The regularized Siegel-Weil formula (the second term identity) and the Rallis inner product formula. Invent. Math. 198(3), 739–831 (2014)
5. Gelbart, S., Jacquet, H.: A relation between automorphic representations of $${\rm GL}(2)$$ and $${\rm GL}(3)$$. Ann. Sci. École Norm. Sup. (4) 11(4), 471–542 (1978)
Cited by
1 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献