Related papers: A Thin Fundamental Set for SL(2, Z)

We consider functionals given by the sum of the perimeter and the double integral of some kernel $g:\mathbb R^N\times\mathbb R^N\to \mathbb R^+$, multiplied by a "mass parameter" $\varepsilon$. We show that, whenever $g$ is admissible,…

Let G be a semi-simple algebraic group over a finitely generated field K of characteristic zero, and let \Gamma < G(K) be a finitely generated Zariski-dense subgroup. In this note we prove that the set of K-generic elements of \Gamma (whose…

Let $\mathfrak{g}$ be a simple Lie algebra: its dual space $\mathfrak{g}^*$ is a Poisson variety. It is well known that for each nilpotent element $f$ in $\mathfrak{g}$, it is possible to construct a new Poisson structure by Hamiltonian…

Let $f$ and $g$ be spectrally normalized holomorphic newforms of even weight $k \geq2$ on $\Gamma_0(q)$. If $f\neq g$, then assume that $q$ is squarefree. For a nice test function $\psi$ supported on $\Gamma_0(1)\backslash\mathbb{H}$, we…

We prove inequalities of Hardy type for functions in Triebel-Lizorkin spaces $F^s_{pq}(G)$ on a domain $G\subset\mathbb{R}^n$, whose boundary has the Aikawa dimension strictly less than $n-sp$.

Let $G/H$ be a homogeneous space of reductive type with non-compact $H$. The study of deformations of discontinuous groups for $G/H$ was initiated by T.~Kobayashi. In this paper, we show that a standard discontinuous group $\Gamma$ admits a…

In this work, we construct fundamental domains for congruence subgroups of $SL_2(F_q[t])$ and $PGL_2(F_q[t])$. Our method uses Gekeler's description of the fundamental domains on the Bruhat- Tits tree $X = X_{q+1}$ in terms of cosets of…

Let $\Gamma$ be a non-uniform lattice in $SL(2, \mathbb R)$. In this paper, we study various $L^2$-norms of automorphic representations of $SL(2, \mathbb R)$. We bound these norms with intrinsic norms defined on the representation.…

Let $f \in S_{2r}(\Gamma_0(N))$ be a normalized newform of weight $2r$ which is good at $p$. Let $K$ be an imaginary quadratic field of class number one in which every prime divisor of $pN$ splits. Let $\chi$ be an anticyclotomic Hecke…

The main goal of this paper is to prove the following theorem: Let $\frak k$ be an $\frak {sl}_2$-subalgebra of a semisimple Lie algebra $\frak g$, none of whose simple factors is of type $A1$. Then there exists a positive integer $b(\frak…

We introduce the notion of set-decomposition of a normal G-flat chain. We show that any normal rectifiable $G$-flat chain admits a decomposition in set-indecomposable sub-chains. This generalizes the decomposition of sets of finite…

We develop practical tools for analyzing the configuration set $F(G,k)$ of $k\geq 2$ distinct elements in a group $G$. We apply our results to design homogeneous linear systems in $\mathbb{F}_q$ that admit nontrivial solutions. Furthermore,…

We present a set of formulae to extract the longitudinal deep inelastic structure function $F_L$ from the transverse structure function $F_2$ and its derivative $dF_2/dlnQ^2$ at small $x$. Using $F_2$ HERA data we obtain $F_L$ in the range…

Let G be a finite abelian group. We examine the discrepancy between subspaces of l^2(G) which are diagonalized in the standard basis and subspaces which are diagonalized in the dual Fourier basis. The general principle is that a Fourier…

We consider a representation of a finitely generated CAT(--K) group $\Gamma$ in SL(d, R) that is Zariski dense and k-Anosov for at least two values of k. We exhibit a gap for the Minkowski dimension of minimal sets for the action of…

Let $\Gamma(n,k)$ be the Grassmann graph formed by the $k$-dimensional subspaces of a vector space of dimension $n$ over a field $\mathbb F$ and, for $t\in \mathbb{N}\setminus \{0\}$, let $\Delta_t(n,k)$ be the subgraph of $\Gamma(n,k)$…

Let $ H $ be a subgroup of a finite group $ G $. We say that $ H $ satisfies the partial $ \Pi $-property in $ G $ if if there exists a chief series $ \varGamma_{G}: 1 =G_{0} < G_{1} < \cdot\cdot\cdot < G_{n}= G $ of $ G $ such that for…

:Let G be a group together with an descending nested sequence of normal subgroups G=G_0, G_1, G_2 G_3, ... of finite index [G:G_k] such the intersection of the G_k-s is the trivial group. Let (X,Y) be a compact 4n-dimensional Poincare' pair…

We give a complete and self-contained proof of a folklore theorem which says that in an Alexandrov space the distance between a point $\gamma(t)$ on a geodesic $\gamma$ and a compact set $K$ is a right-differentiable function of $t$.…

Let $G$ be a connected semisimple simply connected Lie group with a compact Cartan subgroup and let $\Gamma$ be a uniform lattice in $G$. Let $\widehat{G}_d$ denote the set of equivalence classes of unitary discrete series representations…