6 citations · 15 across the 12 of their papers we have counts for
12 papers
Fourier transform and endoscopic transfer on real Lie algebras
Cheng Chen, Zhilin Luo
We prove that the endoscopic transfer on real Lie algebras exists and commutes with the Fourier transform, using methods that are purely local.
Nonabelian Fourier Kernels on and
Zhilin Luo, Ngo Bao Chau
For or , we present explicit formulas for the nonabelian Fourier kernels on , as conjectured by A. Braverman and D. Kazhdan. Additionally, we fu…
Relative Dolbeault Geometric Langlands via the Regular Quotient
Thomas Hameister, Zhilin Luo, Benedict Morrissey
Let be an affine homogeneous spherical variety with abelian regular centralizer and no type N roots. In this paper, we formulate a relative geometric Langlands conjecture…
The local Gross-Prasad conjecture over : Epsilon dichotomy
Cheng Chen, Zhilin Luo
Following the work of Jean-Loup Waldspurger, we prove the epsilon dichotomy part of the local Gross-Prasad conjecture over for tempered local -parameters.
Bias of Root Numbers for Hilbert Newforms of Cubic Level
Zhilin Luo, Qinghua Pi, Han Wu
We give a general formula of the bias of root numbers for Hilbert modular newforms of cubic level. Explicit calculation is given when the base field is $\mathbb{Q}, \mathbb{Q}(\sqr…
Certain Fourier Operators and their Associated Poisson Summation Formulae on
Dihua Jiang, Zhilin Luo
In this paper, we explore a possibility to utilize harmonic analysis on $\GL_1$ to understand Langlands automorphic -functions in general, as a vast generalization of the pionee…
Certain Fourier Operators on and Local Langlands Gamma functions
Dihua Jiang, Zhilin Luo
For a split reductive group over a number field , let be an -dimensional complex representation of its complex dual group . For any irreducible cu…
A Local Trace Formula for the Local Gan-Gross-Prasad Conjecture for Special Orthogonal Groups
Zhilin Luo
Through combining the work of Jean-Loup Waldspurger (\cite{waldspurger10} and \cite{waldspurgertemperedggp}) and Raphaël Beuzart-Plessis (\cite{beuzart2015local}), we give a proof…
Harmonic Analysis and Gamma Functions on Symplectic Groups
Dihua Jiang, Zhilin Luo, Lei Zhang
Over a -adic local field of characteristic zero, we develop a new type of harmonic analysis on an extended symplectic group . It is a…
On the Stable Transfer for Lifting of
Daniel Johnstone, Zhilin Luo
Following the paradigm of \cite{MR3117742}, we are going to explore the stable transfer factors for lifting from to over an…
On the Braverman-Kazhdan Proposal for Local Factors: Spherical Case
Zhilin Luo
In this paper, we study the Braverman-Kazhdan proposal for the local spherical situation. In the -adic case, we give a definition of the spherical component of conjectural space…
On Maximum Norm of Exterior Product and A Conjecture of C.N. Yang
Zhilin Luo
Let be a finite dimensional inner product space over with dimension , where , be the exterior algebra of , the problem is to f…