Journal ArticleDOI
Uniform pointwise bounds for matrix coefficients of unitary representations and applications to Kazhdan constants
Reads0
Chats0
TLDR
In this paper, the authors constructed new uniform pointwise bounds for the matrix coefficients of all infinite-dimensional irreducible unitary representations of a connected reductive linear algebraic group defined over a local field of characteristic not $2.Abstract:
Let $k$ be a local field of characteristic not $2$, and let $G$ be the group of $k$-rational points of a connected reductive linear algebraic group defined over $k$ with a simple derived group of $k$-rank at least $2$. We construct new uniform pointwise bounds for the matrix coefficients of all infinite-dimensional irreducible unitary representations of $G$. These bounds turn out to be optimal for ${\rm SL}\sb n(k), n\geq 3$, and ${\rm Sp}\sb {2n}(k),n\geq 2$. As an application, we discuss a simple method of calculating Kazhdan constants for various compact subsets of semisimple $G$.read more
Citations
More filters
Journal ArticleDOI
The subconvexity problem for GL2
TL;DR: In this article, the authors solve the subconvexity problem for the L-functions of GL-1 and GL-2 automorphic representations over a fixed number field, uniformly in all aspects.
Journal ArticleDOI
Sparse equidistribution problems, period bounds and subconvexity
TL;DR: In this paper, the authors introduce a geometric method to bound periods of automorphic forms using equidistribution results in place of mean value theorems, and the systematic use of mixing and the spectral gap.
Journal ArticleDOI
Hecke operators and equidistribution of Hecke points
Posted Content
On the growth of $L^2$-invariants for sequences of lattices in Lie groups
Miklós Abért,Nicolas Bergeron,Ian Biringer,Tsachik Gelander,Nikolay Nikolov,Jean Raimbault,Iddo Samet +6 more
TL;DR: In this paper, the authors study the asymptotic behavior of Betti numbers, twisted torsion and other spectral invariants of sequences of locally symmetric spaces and show that BS-convergence implies convergence, in an appropriate sense, of the associated normalized relative Plancherel measures.
Book
The Ergodic Theory of Lattice Subgroups
Alexander Gorodnik,Amos Nevo +1 more
TL;DR: In this paper, the authors prove mean and pointwise ergodic theorems for general families of averages on a semisimple algebraic group G, together with an explicit rate of convergence when the action has a spectral gap.
References
More filters
Book
Groupes et algèbres de Lie
TL;DR: Les Elements de mathematique de Nicolas Bourbaki ont pour objet une presentation rigoureuse, systematique et sans prerequis des mathematiques depuis leurs fondements as mentioned in this paper.
BookDOI
Discrete subgroups of semisimple Lie groups
TL;DR: The Structure of the Book as discussed by the authors is a collection of essays about algebraic groups over arbitrary fields, including a discussion of the relation between the structure of closed subgroups and property (T) of normal subgroups.
Book
Ergodic Theory and Semisimple Groups
TL;DR: In this paper, a generalization to p-adic groups and S-arithmetic groups is presented. But the generalization is not applicable to algebraic groups with Borel spaces.
Book
Basic Number Theory
TL;DR: In this article, the authors define a classfield theory for algebraic number-fields with respect to simple algebras over A-fields and the Brauer group of a local field.
Book
Representation of Lie groups and special functions
A. U. Klimyk,N. Ya. Vilenkin +1 more
TL;DR: The theory of elliptic integrals was introduced by Abel as discussed by the authors, who proposed a special function to evaluate integrals, which is called integral sine, logarithm, exponential function, probability integral and so on.