On Critical Values of L-functions of Potentially Automorphic Motives

نویسندگان

  • DANIEL BARRERA
  • LUCIO GUERBEROFF
چکیده

In this paper we prove a version of Deligne’s conjecture for potentially automorphic motives, twisted by certain algebraic Hecke characters. The Hecke characters are chosen in such a way that we can use automorphic methods in the context of totally definite unitary groups.

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

On tensor product $L$-functions and Langlands functoriality

‎In the spirit of the Langlands proposal on  Beyond Endoscopy ‎we discuss the explicit relation between the Langlands functorial transfers and automorphic $L$-functions‎. ‎It is well-known that the poles of the $L$-functions have deep impact to the Langlands functoriality‎. ‎Our discussion also‎ ‎includes the meaning of the central value of the tensor product $L$-functions in terms of the Langl...

متن کامل

Automorphic Galois representations and the cohomology of Shimura varieties

The first part of this report describes the class of representations of Galois groups of number fields that have been attached to automorphic representations. The construction is based on the program for analyzing cohomology of Shimura varieties developed by Langlands and Kottwitz. Using p-adic methods, the class of Galois representations obtainable in this way can be expanded slightly; the lin...

متن کامل

Mollification of the fourth moment of automorphic L-functions and arithmetic applications

In this paper, we compute the twisted fourth power moment of modular L-functions of prime level near the critical line. This allows us to prove some new non-vanishing results on the central values of automorphic L-functions, in particular whose obtained by base change from GL2(Q) to GL2(K) for K a cyclic field of low degree.

متن کامل

Moduli Fields of Cm-motives Applied to Hilbert's 12-th Problem

We apply the theorem of Shimura and Taniyama to compute the largest abelian extension of a CM-eld E which can be obtained by evaluating E-rational automorphic functions at certain special points of Shimura varieties. Abelian class eld theory classiies the abelian extensions of a number eld k, but does not explain how to generate the elds. In his Jugendtraum, Kronecker suggested that the abelian...

متن کامل

A Trace Formula of Special Values of Automorphic L-functions

Deligne introduced the concept of special values of automorphic L-functions. The arithmetic properties of these L-functions play a fundamental role in modern number theory. In this paper we prove a trace formula which relates special values of the Hecke, Rankin, and the central value of the Garrett triple L-function attached to primitive newforms. This type of trace formula is new and involves ...

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 2016