ﻻ يوجد ملخص باللغة العربية
In this paper, we study top Fourier coefficients of certain automorphic representations of $mathrm{GL}_n(mathbb{A})$. In particular, we prove a conjecture of Jiang on top Fourier coefficients of isobaric automorphic representations of $mathrm{GL}_n(mathbb{A})$ of form $$ Delta(tau_1, b_1) boxplus Delta(tau_2, b_2) boxplus cdots boxplus Delta(tau_r, b_r),, $$ where $Delta(tau_i,b_i)$s are Speh representations in the discrete spectrum of $mathrm{GL}_{a_ib_i}(mathbb{A})$ with $tau_i$s being unitary cuspidal representations of $mathrm{GL}_{a_i}(mathbb{A})$, and $n = sum_{i=1}^r a_ib_i$. Endoscopic lifting images of the discrete spectrum of classical groups form a special class of such representations. The result of this paper will facilitate the study of automorphic forms of classical groups occurring in the discrete spectrum.
We study the question of Eulerianity (factorizability) for Fourier coefficients of automorphic forms, and we prove a general transfer theorem that allows one to deduce the Eulerianity of certain coefficients from that of another coefficient. We also
In this paper we analyze Fourier coefficients of automorphic forms on a finite cover $G$ of an adelic split simply-laced group. Let $pi$ be a minimal or next-to-minimal automorphic representation of $G$. We prove that any $etain pi$ is completely det
We consider a general class of Fourier coefficients for an automorphic form on a finite cover of a reductive adelic group ${bf G}(mathbb{A}_{mathbb{K}})$, associated to the data of a `Whittaker pair. We describe a quasi-order on Fourier coefficients,
Let $G$ be a group and $H$ be a subgroup of $G$. The classical branching rule (or symmetry breaking) asks: For an irreducible representation $pi$ of $G$, determine the occurrence of an irreducible representation $sigma$ of $H$ in the restriction of $
We show that Fourier coefficients of automorphic forms attached to minimal or next-to-minimal automorphic representations of ${mathrm{SL}}_n(mathbb{A})$ are completely determined by certain highly degenerate Whittaker coefficients. We give an explici