Notes on automorphic functions: an entire automorphic form of positive dimension is zero

نویسندگان

چکیده

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Notes on Automorphic Functions: An Entire Autol!lorphic Form of Positive Dimension is Zero*

L It is a result familiar in the theory of automorphic form s that an entire automorphic form of positive dimension on an H-group is identically zero (see sec. 2 for the definitions). This follows immediately , for exa mple, from the well-known exac t formula for the Fourier coefficie nts of automorphic forms of positive dimension ([1], p. 314).1 Another proof is by means of a formula for the n...

متن کامل

On Automorphic Functions

Let r c PSL(2, JR.) be a discrete subgroup with quotient r\H offinite volume but not compact. The spectrum of the Laplacian on L 2 auto-morphic functions is unstable under perturbations; however, it becomes muchmore manageable when the scattering frequencies are adjoined (with multiplic-ity equal to the order of the pole of the determinant of the scattering matrixat these po...

متن کامل

Lectures on automorphic L-functions

PREFACE This article follows the format of five lectures that we gave on automorphic Lfunctions. The lectures were intended to be a brief introduction for number theorists to some of the main ideas in the subject. Three of the lectures concerned the general properties of automorphic L-functions, with particular reference to questions of spectral decomposition. We have grouped these together as ...

متن کامل

Estimates of Automorphic Functions

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 general method which gives an estimate on the average of the au...

متن کامل

The Dimension of Spaces of Automorphic Forms

1. The trace formula of Selberg reduces the problem of calculating the dimension of a space of automorphic forms, at least when there is a compact fundamental domain, to the evaluation of certain integrals. Some of these integrals have been evaluated by Selberg. An apparently different class of definite integrals has occurred in Harish-Chandra’s investigations of the representations of semi-sim...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

ژورنال

عنوان ژورنال: Journal of Research of the National Bureau of Standards Section B Mathematics and Mathematical Physics

سال: 1967

ISSN: 0022-4340

DOI: 10.6028/jres.071b.022