Survey on Automorphic Period for General Bessel Model
نویسنده
چکیده
Let F be a number field with ring of adèles A and the set of places Σ. Fix a nontrivial character ψ : F\A → C×. Throughout the note, for a linear algebraic group G over F , we always use the Tamagawa measure dg on G(A). In particular, the volume of G(F )\G(A) is 1 if G is unipotent. Consider a reductive group G over F and a closed F -subgroup H. Denote A(G) the space of automorphic forms on G(A) and Acusp(G) the subspace of cusp forms, both being representations of G(A) via the right translation. Let ν : H(F )\H(A)→ C×
منابع مشابه
The Bessel Period Functional on So5: the Nontempered Case
For automorphic representations in the nontempered cuspidal spectrum of SO5, we establish a precise Bessel period formula, in which the square of the global Bessel period is decomposed as an Euler product of regularized local Bessel period integrals of matrix coefficients.
متن کاملRefined global Gan–Gross–Prasad conjecture for Bessel periods
We formulate a refined version of the global Gan–Gross–Prasad conjecture for general Bessel models, extending the work of Ichino–Ikeda and R. N. Harris in the co-rank 1 case. It is an explicit formula relating the automorphic period of Bessel type and the central value of certain L-function. To support such conjecture, we provide two examples for pairs SO5 SO2 and SO6 SO3 (both co-rank 3) in th...
متن کامل0 O ct 1 99 4 EXPLICIT FORMULAS FOR THE WALDSPURGER AND BESSEL MODELS
In this paper we will study certain models of irreducible admissible representations of the split special orthogonal group SO(2n + 1) over a nonarchimedean local field. If n = 1, these models were considered by Waldspurger [Wa1,Wa2], and arose in his profound studies of the Shimura correspondence. If n = 2, they were considered by Novodvorsky and Piatetski-Shapiro [NP], who called them Bessel m...
متن کاملA method for computing general automorphic forms on general groups
The purpose of this note is to describe a method for computing general automorphic forms. I have carried out only limited computational tests so far, and have not discovered any new automorphic forms using it. However, the method does identify some lifted cusp forms on GL(3) and until recently was the only general method to compute an automorphic form on a higher rank group. It generalizes the ...
متن کاملExplicit Formulas for Thewaldspurger and Bessel
In this paper we will study certain models of irreducible admissible representations of the split special orthogonal group SO(2n + 1) over a nonarchimedean local eld. If n = 1, these models were considered by Waldspurger Wa1,Wa2], and arose in his profound studies of the Shimura correspondence. If n = 2, they were considered by Novodvorsky and Piatetski-Shapiro NP], who called them Bessel model...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2013