ESTIMATES OF AUTOMORPHIC FUNCTIONS

By J. Bernstein, A. Reznikov. 2003

66 citations recorded by the source corpus.

We present a new method to estimate trilinear period for automorphic representations of SL2(R). The method is based on the uniqueness principle in representation theory. We show how to separate the exponentially decaying factor in the triple period from the essential automorphic factor which behaves polynomially. We also describe a gen- eral method which gives an estimate for the average of the automorphic factor and thus prove a convexity bound for the triple period. 2000 Math. Subj. Class. 11F67, 11F70, 22E45.

Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/ff263befff6e42f47b1e461721294856e23b1bf1

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In Algebra and Number Theory

1. T. Oshima
2. A. Reznikov
3. Toshiyuki Kobayashi
4. M. Pevzner

In Discrete Mathematics and Combinatorics

1. Toshiyuki Kobayashi
2. A. Reznikov
3. T. Matsuki

In Mathematical Physics

1. Toshiyuki Kobayashi
2. T. Oshima
3. A. Reznikov
4. M. Pevzner
5. T. Matsuki
6. Christopher D. Sogge

Citations in the corpus

• Norms of geodesic restrictions for eigenfunctions on hyperbolic surfaces and representation theory (2004, methodology): “tant Cℓ such that for any eigenfunction φi with the eigenvalue µi the following bound holds pℓ(φi) ≤ Cℓ ·µ 1 4 (2) i . 1 2 ANDRE REZNIKOV 1.3. The method. We follow the general strategy introduced in [BR3]. It is based on ideas from representation theory. Namely, any Riemannian surface Y gives rise ”
• Finite multiplicity theorems for induction and restriction (2011, background): “The condition (HP) in the triple product pair has laid a solid foundation of concrete analysis of the tensor product of two representations (see [3] for (8)G = SL(2,R); [7] for (8)G = SO(n, 1), for instance).”