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2004•Moscow Mathematical JournalRequires access

Estimates of Automorphic Functions

Joseph Bernstein, Alexander Reznikov

Open publisher page 55 citations

Abstract

We present a new method of estimating 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 general method which gives an estimate on the average of the automorphic factor and thus prove a convexity bound for the triple period. .

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What this paper is about

We present a new method of estimating 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 general method which gives an estimate on the average of the automorphic factor and thus prove a convexity bound for the triple period. .

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OpenAlex reports 55 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

We present a new method of estimating 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 general method which gives an estimate on the average of the automorphic factor and thus prove a convexity bound for the triple period. .

Key concepts: Mathematics, Automorphic form, Pure mathematics

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