Existence and Weyl’s law for spherical cusp forms
By Elon Lindenstrauss, Akshay Venkatesh. 2005
69 citations recorded by the source corpus.
Abstract.Let G be a split adjoint semisimple group over $${\user2{\mathbb{Q}}} $$ and $$ K _\infty \subset \mathbf{G} \user2{\mathbb{(R)}} $$ a maximal compact subgroup. We shall give a uniform, short and essentially elementary proof of the Weyl law for cusp forms on congruence quotients of $$ {\mathbf{G}}({\user2{\mathbb{R}}})/K_{\infty } $$ . This proves a conjecture of Sarnak for $$ \user2{\mathbb{Q}} $$ -split groups, previously known only for the case G = PGL(n). The key idea amounts to a new type of simple trace formula.
Subfields: Algebra and Number Theory, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/f1ef392a780c1579967afa3d764da5a37d149503
How researchers see this paper
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In Algebra and Number Theory
- Erez Lapid
- Manfred Einsiedler
- Elon Lindenstrauss
- Werner Mueller
- Akshay Venkatesh
- Lior Silberman
- P. Michel
- R. Munshi
In Mathematical Physics
- Manfred Einsiedler
- Akshay Venkatesh
- Elon Lindenstrauss
- Erez Lapid
- Lior Silberman
- Werner Mueller
- P. Michel
- Kannan Soundararajan
Citations in the corpus
- On Quantum Unique Ergodicity for Locally Symmetric Spaces (2004, result): “(It is likely that one could establish similar results in a somewhat more general setting using the technique of [ LV ]).”
- Diagonal actions on locally homogeneous spaces (2008, methodology): “This idea can be used to give an alternative elementary proof of the existence of cusp forms [LV07].”
- SPECTRAL ASYMPTOTICS FOR ARITHMETIC QUOTIENTS OF SL(n,R)/SO(n) (2007, methodology): “For the spherical spectrum, Lindenstrauss and Venkatesh ([LV07]) showed that Weyl’s law holds in great generality, proving a conjecture of Sarnak.”