论文标题
$ PGL_4 $的标准非均匀算术商的弱ramanujan属性
Weak Ramanujan property of the standard non-uniform arithmetic quotient of $PGL_4$
论文作者
论文摘要
令$ f $为有限字段的正式系列，$ \ nathcal {b} _d $是与$ pgl_d（f）$相关的仿型建筑物。给定$ pgl_d（f）$中的晶格$γ$，如果每一个非闲置离散的同时偶然的邻接邻接型运算符，则称为$γ\ backslash \ mathcal {b} _d $，称为弱ramanujan $ l^2（γ\ backslash \ mathcal {b} _d）$包含在那些作用于$ l^2（\ Mathcal {b}）$的操作员的同时频谱中。在本文中，我们证明了标准的非均匀算术商$ pgl_4（\ mathbb {f} _q [t]）\ backslash \ mathcal {b} _4 $ of $ pgl_4（f）$是弱的ramanujan。
Let $F$ be a field of formal series over a finite field and $\mathcal{B}_d$ be the affine building associated to $PGL_d(F)$. Given a lattice $Γ$ in $PGL_d(F)$, the complex arising as a quotient $Γ\backslash \mathcal{B}_d$ is called weakly Ramanujan if every non-tivial discrete simultaneous spectrum of the colored adjacency operators $A_1,A_2,\ldots,A_{d-1}$ acting on $L^2(Γ\backslash \mathcal{B}_d)$ is contained in the simultaneous spectrum of those operators acting on $L^2(\mathcal{B})$. In this paper, we prove that the standard non-uniform arithmetic quotient $PGL_4(\mathbb{F}_q[t])\backslash \mathcal{B}_4$ of $PGL_4(F)$ is weakly Ramanujan.
