Some New Results on the Eichler Cohomology of Automorphic Forms

نویسنده

  • M. I
چکیده

We here formulate and prove several new results concerning the Eichler cohomology of automorphic forms on finitely generated Fuchsian groups of the first kind and, in particular, on //-groups. The Eichler cohomology we introduce is connected with automorphic forms of arbitrary real degree (as opposed to integral degree), with a suitably chosen underlying space of functions analytic in the upper half-plane. We obtain structure theorems for the Eichler cohomology groups which are analogous to earlier results of Eichler and Gunning.

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

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Week 2: Betti Cohomology of Shimura Varieties — the Matsushima Formula

Rough exposition of the goal of this course. Hecke actions on Shimura varieties and their cohomology groups. The Matsushima formula in the classical setting; relative Lie algebra cohomology, spectral decomposition on L(Γ\G). The Matsushima formula in the adelic setting — automorphic representations appear in the Betti cohomology of Shimura varieties. Admissible (g, U)-modules and cohomological ...

متن کامل

Modular Forms and - adic Representations ∗

the circumstance that L-functions can be introduced not only in the context of automorphic forms, with which he has had some experience, but also in the context of diophantine geometry. That this circumstance can be the source of deep problems was, I believe, first perceived by E. Artin. He was, to be sure, concerned with forms on GL(1) and with varieties of dimension 0. This remains the only c...

متن کامل

Modular Forms and Elliptic Curves over Q(ζ 5 )

Let ζ5 be a primitive fifth root of unity, and let F = Q(ζ5). In this talk we describe recent computational work that investigates the modularity of elliptic curves over F . Here by modularity we mean that for a given elliptic curve E over F with conductor N there should exist an automorphic form f on GL2, also of conductor N , such that we have the equality of partial L-functions LS(s, f) = LS...

متن کامل

Weight Reduction for Mod l Bianchi Modular Forms

LetK be an imaginary quadratic field with class number one. We prove that mod l, a system of Hecke eigenvalues occurring in the first cohomology group of some congruence subgroup Γ of SL2(ØK) can be realized, up to twist, in the first cohomology with trivial coefficients after increasing the level of Γ by (l). 1. Motivation and Summary Let G be a connected semisimple algebraic group defined ove...

متن کامل

Everywhere Unramified Automorphic Cohomology for Sl(3,z)

We conjecture that the only irreducible cuspidal automorphic representations for GL(3)/Q of cohomological type and level 1 are (up to twisting) the symmetric square lifts of classical cuspforms on GL(2)/Q of level 1. We present computational evidence for this conjecture. 1. Statement and explanation of a conjecture Arithmetic objects defined over Q and unramified everywhere are rare. For exampl...

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

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

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2007