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

This paper compares the divisorial gonality of a finite graph $G$ to the divisorial gonality of the associated metric graph $\Gamma(G,\mathbb{1})$ with unit lengths. We show that $\text{dgon}(\Gamma(G,\mathbb{1}))$ is equal to the minimal…

Iwasawa's theorem indicates that a finite group $G$ is supersolvable if and only if all maximal chains of the identity in $G$ have the same length. As generalizations of Iwasawa's theorem, we provide some characterizations of the structure…

This note constructs an explicit normal boundary dilation for a commuting pair $(S,P)$ of bounded operators with the symmetrized bidisk $$\Gamma=\{(z_1+z_2,z_1z_2):|z_1|,|z_2| \leq 1\}$$ as a spectral set. Such explicit dilations had…

Let $f$ and $g$ be holomorphic or Maass cusp forms for $\rm SL_2(\mathbb{Z})$ and let $\chi$ be a primitive Dirichlet character of prime power conductor $\mathfrak{q}=p^{\kappa}$ with $p$ prime and $\kappa>12$. A subconvex bound for the…

Let $(G,G^\Gamma)$ be a Klein four symmetric pair. The author wants to classify all the Klein four symmetric pairs $(G,G^\Gamma)$ such that there exists at least one nontrivial unitarizable simple $(\mathfrak{g},K)$-module $\pi_K$ that is…

The Gruenberg-Kegel graph $\Gamma(G)$ of a finite group $G$ is the graph whose vertex set is the set of prime divisors of $|G|$ and in which two distinct vertices $r$ and $s$ are adjacent if and only if there exists an element of order $rs$…

We describe the determination of the DIS structure functions $F_{2}$ and $F_{L}$ by using the singlet Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) and Altarelli-Martinelli equations at small values of $x$. The determination of the…

We present here a shorter version of the proof of a result from our paper ``On a class of type II$_1$ factors with Betti numbers invariants'', showing that the von Neumann factor associated with the group $\Bbb Z^2 \rtimes SL(2, \Bbb Z)$…

Given a finite group $G$, we say that $G$ has weak normal covering number $\gamma_w(G)$ if $\gamma_w(G)$ is the smallest integer with $G$ admitting proper subgroups $H_1,\ldots,H_{\gamma_w(G)}$ such that each element of $G$ has a conjugate…

This is an attempt at a practical and essentially self-contained theory of automorphic representations in the framework $$\hbox{$L^2(\varGamma\backslash\r{G})$ with $\r{G}=\r{PSL}(2,\B{R})$ and $\varGamma=\r{PSL}(2,\B{Z})$.}$$

Let $ f_0 $ and $ f_\infty $ be formal power series at the origin and infinity, and $ P_n/Q_n $, with $ \mathrm{deg}(P_n),\mathrm{deg}(Q_n)\leq n $, be a rational function that simultaneously interpolates $ f_0 $ at the origin with order $…

We prove a variety of results concerning singular sets of reals. Our results concern: Kysiak and Laver-null sets, Kocinac and gamma-k-sets, Fleissner and square Q-sets, Alikhani-Koopaei and minimal Q-like-sets, Rubin and sigma-sets, and…

Let $F$ be a local non-archimedian field, $G$ a semisimple $F$-group, $dg$ a Haar measure on $G$ and $\mathcal S(G)$ be the space of locally constant complex valued functions $f$ on $G$ with compact support. For any regular elliptic…

We first construct a real family of $SL(2,\mathbb{R})$-invariant symbol composition product $\{\sharp_\theta\}_{\theta\in,\mathbb{R}}$ on the analogue of the Schwartz space $S(\mathbb{D})$ on the hyperbolic plane…

Let $\mathcal{F}$ denote the set of functions $f \colon [-1/2,1/2] \to \mathbb{R}$ such that $\int f = 1$. We determine the value of $\inf_{f \in \mathcal{F}} \| f \ast f \|_2$ up to a 0.0014\% error, thereby making progress on a problem…

Given an increasing integer sequence $(a_n)$, a real number $\alpha$, and a sequence $\psi(n)$, we study the set $W$ of real numbers $\gamma$ for which $a_n\alpha - \gamma$ is a distance less than $\psi(n)$ away from an integer. This is…

Let $\Lambda<SL(2,\mathbb{Z})$ be a finitely generated, non-elementary Fuchsian group of the second kind, and $v, w$ be two primitive vectors in $\mathbb{Z}^2-(0,0)$. We consider the set $\mathcal{S}=\{\langle…

We prove that for every number k each countable infinite group $G$ admits a partition $G=A\cup B$ into two sets which are $k$-meager in the sense that for every $k$-element subset $K\subset G$ the sets $KA$ and $KB$ are not thick. The proof…

The main result of this paper is that an entire function $f$ that is in $L^2(\mathbb C^n,\psi)$ with respect to the weight $\psi(z)=2mH_S(z)+\gamma\log(1+|z|^2)$ is a polynomial with exponents in $m\widehat S_\Gamma$. Here $H_S$ is the…

Let $\mathcal{G}$ be a smooth linear group scheme of finite type. For any positive integer $k$ and a finite field $\mathbb{F}$, let $W_k(\mathbb{F})$ be the ring of Witt vectors of length $k$ over $\mathbb{F}$. We show that the group…