ترغب بنشر مسار تعليمي؟ اضغط هنا

On Sarnaks Density Conjecture and its Applications

216   0   0.0 ( 0 )
 نشر من قبل Amitay Kamber
 تاريخ النشر 2020
  مجال البحث
والبحث باللغة English




اسأل ChatGPT حول البحث

Sarnaks Density Conjecture is an explicit bound on the multiplicities of non-tempered representations in a sequence of cocompact congruence arithmetic lattices in a semisimple Lie group, which is motivated by the work of Sarnak and Xue. The goal of this work is to discuss similar hypotheses, their interrelation and applications. We mainly focus on two properties - the Spectral Spherical Density Hypothesis and the Geometric Weak Injective Radius Property. Our results are strongest in the p-adic case, where we show that the two properties are equivalent, and both imply Sarnaks General Density Hypothesis. One possible application is that either the limit multiplicity property or the weak injective radius property imply Sarnaks Optimal Lifting Property. Conjecturally, all those properties should hold in great generality. We hope that this work will motivate their proofs in new cases.



قيم البحث

اقرأ أيضاً

181 - Taekyun Kim 2008
Recently the new q-Euler numbers are defined. In this paper we derive the the Kummer type congruence related to q-Euler numbers and we introduce some interesting formulae related to these q-Euler numbers.
77 - Zijian Yao 2018
Let $K$ be a local function field of characteristic $l$, $mathbb{F}$ be a finite field over $mathbb{F}_p$ where $l e p$, and $overline{rho}: G_K rightarrow text{GL}_n (mathbb{F})$ be a continuous representation. We apply the Taylor-Wiles-Kisin metho d over certain global function fields to construct a mod $p$ cycle map $overline{text{cyc}}$, from mod $p$ representations of $text{GL}_n (mathcal{O}_K)$ to the mod $p$ fibers of the framed universal deformation ring $R_{overline{rho}}^square$. This allows us to obtain a function field analog of the Breuil--Mezard conjecture. Then we use the technique of close fields to show that our result is compatible with the Breuil-Mezard conjecture for local number fields in the case of $l e p$, obtained by Shotton.
We establish the local Langlands conjecture for small rank general spin groups $GSpin_4$ and $GSpin_6$ as well as their inner forms. We construct appropriate $L$-packets and prove that these $L$-packets satisfy the properties expected of them to the extent that the corresponding local factors are available. We are also able to determine the exact sizes of the $L$-packets in many cases.
We introduce a generalized $k$-FL sequence and special kind of pairs of real numbers that are related to it, and give an application on the integral solutions of a certain equation using those pairs. Also, we associate skew circulant and circulant ma trices to each generalized $k$-FL sequence, and study the determinantal variety of those matrices as an application.
143 - Hai-Liang Wu , Yue-Feng She 2020
Let $p>3$ be a prime. Gauss first introduced the polynomial $S_p(x)=prod_{c}(x-zeta_p^c),$ where $0<c<p$ and $c$ varies over all quadratic residues modulo $p$ and $zeta_p=e^{2pi i/p}$. Later Dirichlet investigated this polynomial and used this to sol ve the problems involving the Pell equations. Recently, Z.-W Sun studied some trigonometric identities involving this polynomial. In this paper, we generalized their results. As applications of our result, we extend S. Chowlas result on the congruence concerning the fundamental unit of $mathbb{Q}(sqrt{p})$ and give an equivalent form of the extended Ankeny-Artin-Chowla conjecture.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا