Related papers: Schwarz Lemma for the tetrablock

We study zeta functions enumerating submodules invariant under a given endomorphism of a finitely generated module over the ring of ($S$-)integers of a number field. In particular, we compute explicit formulae involving Dedekind zeta…

We give a proof of the geometric fundamental lemma of Kottwitz. As explained by Laumon, this implies the fundamental lemma for the unitary groups.

Let $\Gamma$ denote a distance-regular graph with diameter $D \ge 3$. Assume $\Gamma$ has classical parameters $(D,b,\alpha,\beta)$ with $b < -1$. Let $X$ denote the vertex set of $\Gamma$ and let $A \in MX$ denote the adjacency matrix of…

In this paper we investigate some algebraic and geometric consequences which arise from an extremal bound on the Hilbert function of the general hyperplane section of a variety (Green's Hyperplane Restriction Theorem). These geometric…

We prove that for every flat surface $\omega$, the Hausdorff dimension of the set of directions in which Teichm\"{u}ller geodesics starting from $\omega$ exhibit a definite amount of deviation from the correct limit in Birkhoff's and…

We present a rough path analog of the classical Gronwall Lemma introduced recently by A. Deya, M. Gubinelli, M. Hofmanov\'a, S. Tindel in [arXiv:1604.00437] and discuss two of its applications. First, it is applied in the framework of rough…

We state and prove an equivariant version of Lehmer's conjecture on heights, generalizing papers by Zagier (1993) and Dresden (1998) which are special cases of this theorem. We also extend their three cases to a full classification of all…

We establish an edge of the wedge theorem for the sheaf of holomorphic functions with exponential growth at infinity and construct the sheaf of Laplace hyperfunctions in several variables. We also study the fundamental properties of the…

This work is a purely syntactic geometric exploration of some few elements, which are our axioms, that in last instance it is the set of differential equations whose solutions give the geodesic lines of the Schwarzschild spacetime. We…

We give results exploring the relationship between dominating and unbounded reals in Hechler extensions, as well as the relationships among the extensions themselves. We show that in the standard Hechler extension there is an unbounded real…

The paper is a survey of recent results in analysis of additive functions over function fields motivated by applications to various classes of special functions including Thakur's hypergeometric function. We consider basic notions and…

It is well known that, in the plane, the boundary of any quadrature domain (in the classical sense) coincides with the zero set of a polynomial. We show, by explicitly constructing some four-dimensional examples, that this is not always the…

We offer some new applications of an extension of Abel's lemma, as well as its more general form established by Andrews and Freitas. A nice connection is established between this lemma and series involving the Riemann zeta function.

We deduce the Schaper formula for Hecke-algebras at root of unity from the Jantzen conjecture in the LLT-setup. This explains an observation due to R. Rouquier.

Marden and Strebel established the Heights Theorem for integrable holomorphic quadratic differentials on parabolic Riemann surfaces. We extends the validity of the Heights Theorem to all surfaces whose fundamental group is of the first…

We provide an explicit construction of a cross section for the geodesic flow on infinite-area Hecke triangle surfaces which allows us to conduct a transfer operator approach to the Selberg zeta function. Further we construct closely related…

Let \theta:\pi_1(R) \to \PSL(2,\C) be a homomorphism of the fundamental group of an oriented, closed surface R of genus exceeding one. We will establish the following theorem. Theorem. Necessary and sufficient for \theta to be the monodromy…

In this note we prove a version of the classical Schwarz lemma for the first eigenvalues of the Laplacian with Dirichlet boundary data. A key ingredient in our proof is an isoperimetric inequality for the first eigenfunction, due to Payne…

Quasiconformal homeomorphisms of the whole space Rn, onto itself normalized at one or two points are studied. In particular, the stability theory, the case when the maximal dilatation tends to 1, is in the focus. Our main result provides a…

The Lenz-Sommerfeld argument allows an ingenious and simple derivation of the Schwarzschild solution of Einstein equations of general relativity. In this paper, we use the same reasoning to construct the de Sitter line element.