Related papers: The Dehn Function of PSL(2,Z[1/p])

We show that there is an infinite set of primes $\mathcal{P}$ of density one, such that the family of \textit{all} Cayley graphs of $\mathrm{SL}(2,p)$%, $p\in \mathcal{P}$, is a family of expanders.

It is known that there is no finitely presented group for which the Dehn function lies asymptotically strictly between linear and quadratic functions. This work presents an example of a semigroup that has Dehn function equivalent to $n \log…

For each positive integer n, we determine the set of symmetric functions f for which the congruence f(p/1,p/2,...,p/(p-1)) \equiv 0 mod p^n holds for all sufficiently large primes p. Our determination is conditional on a conjecture…

SDE driven by an $\alpha $-stable process, $\alpha \in \lbrack 1,2),$ with Lipshitz continuous coefficient and $\beta $-H\"older drift is considered. The existence and uniqueness of a strong solution is proved when $\beta >1-\alpha /2$ by…

Let $p<q$ be odd primes, $\rho_1$ and $\rho_2$ be irreducible representations of $\text{SL}(2,\mathbb{Z}_p)$ and $\text{SL}(2,\mathbb{Z}_q)$ of dimensions $\frac{p+1}{2}$ and $\frac{q+1}{2}$, respectively. We show that if…

A version of the fundamental mean-square convergence theorem is proved for stochastic differential equations (SDE) which coefficients are allowed to grow polynomially at infinity and which satisfy a one-sided Lipschitz condition. The…

We extend a theorem by Kleiner, stating that on a group with polynomial growth, the space of harmonic functions of polynomial of at most $k$ is finite dimensional, to the settings of locally compact groups equipped with measures with…

We deal with a class of equations driven by nonlocal, possibly degenerate, integro-differential operators of differentiability order $s\in (0,1)$ and summability growth $p>1$, whose model is the fractional $p$-Laplacian with measurable…

Let $\mathcal{L}_\epsilon$ be a family of elliptic systems of linear elasticity with rapidly oscillating periodic coefficients. We obtain the uniform $W^{1,p}$ estimate in a Lipschitz domain for solutions to the Dirichlet problem, where…

A class P_{n,m,p}(x) of polynomials is defined. The combinatorial meaning of its coefficients is given. Chebyshev polynomials are the special cases of P_{n,m,p}(x). It is first shown that P_{n,m,p}(x) may be expressed in terms of…

This is a contribution to the classification problem for dp-minimal expansions of $(\mathbb{Z},+)$. Let $S$ be a dense cyclic group order on $(\mathbb{Z},+)$. We use results on "dense pairs" to construct uncountably many dp-minimal…

Anderson and Canary have shown that if the algebraic limit of a sequence of discrete, faithful representations of a finitely generated group into PSL(2,C) does not contain parabolics, then it is also the sequence's geometric limit. We…

We prove that the Zassenhaus conjecture is true for $PSL(2,8)$ and $PSL(2,17)$. This is a continuation of research initiated by W. Kimmerle, M. Hertweck and C. H\"ofert.

In this paper, we compute an upper bound for the Dehn function of a finitely presented metabelian group. In addition, we prove that the same upper bound works for the relative Dehn function of a finitely generated metabelian group. We also…

Series of finite dimensional representations of the superalgebras spl(p,q) can be formulated in terms of linear differential operators acting on a suitable space of polynomials. We sketch the general ingredients necessary to construct these…

We demonstrate under appropriate finiteness conditions that a coarse embedding induces an inequality of homological Dehn functions. Applications of the main results include a characterization of what finitely presentable groups may admit a…

An exponential automorphism of $\mathbf{C}$ is a function $\alpha: \mathbf{C} \rightarrow \mathbf{C}$ such that $\alpha(z_1 + z_2) = \alpha(z_1) + \alpha(z_2)$ and $\alpha\left( e^z \right) = e^{\alpha(z)}$ for all $z, z_1, z_2 \in…

Let $P\in \Bbb Q_p[x,y]$, $s\in \Bbb C$ with sufficiently large real part, and consider the integral operator $ (A_{P,s}f)(y):=\frac{1}{1-p^{-1}}\int_{\Bbb Z_p}|P(x,y)|^sf(x) |dx| $ on $L^2(\Bbb Z_p)$. We show that if $P$ is homogeneous…

We classify up to equivalence all finite-dimensional irreducible representations of PSL2(Z) whose restriction to the commutator subgroup is diagonalizable.

For a polynomial P, we consider the sequence of iterated integrals of ln P(x). This sequence is expressed in terms of the zeros of P(x). In the special case of ln(1 + x^2), arithmetic properties of certain coefficients arising are…