Related papers: Automatic meromorphy in non-archimedean geometry

Nevanlinna functions are meromorphic functions with a finite number of asymptotic values and no critical values. In [KK2] it was proved that if the orbits of all the asymptotic values accumulate on a compact set on which the function acts…

Classification and invariants, with respect to basis changes, of finite dimensional algebras are considered. An invariant open, dense (in the Zariscki topology) subset of the space of structural constants is defined. The algebras with…

A meromorphic function on a compact complex analytic manifold defines a $\bc\infty$ locally trivial fibration over the complement of a finite set in the projective line $\bc\bp^1$. We describe zeta-functions of local monodromies of this…

Let D be a bounded domain in the complex plane whose boundary bD consists of finitely many pairwise disjoint real analytic simple closed curves. Let f be an integrable function on bD. In the paper we show how to compute the candidates for…

Let $f : X\to X$ be a dominating meromorphic map on a compact K\"ahler manifold $X$ of dimension $k$. We extend the notion of topological entropy $h^l_{\mathrm{top}}(f)$ for the action of $f$ on (local) analytic sets of dimension $0\leq l…

Using the notion of order convergent nets, we develop an order-theoretic approach to differentiable functions on Archimedean complex $\Phi$-algebras. Most notably, we improve the Cauchy-Hadamard formulas for universally complete complex…

Let X be an affine real algebraic set . We investigate on the theory of algebraically constructible functions on X and the description of the semi-algebraic subsets of X when we replace the polynomial functions on X by some rational…

We prove that every $2$-local automorphism on a finite-dimensional semi-simple Lie algebra $\mathcal{L}$ over an algebraically closed field of characteristic zero is an automorphism. We also show that each finite-dimensional nilpotent Lie…

Let $F$ be a $p$-adic field and let $G$ be a connected reductive group defined over $F$. We assume $p$ is big. Denote $\mathfrak{g}$ the Lie algebra of $G$. To each vertex $s$ of the reduced Bruhat-Tits' building of $G$, we associate as…

A standard theorem in nonsmooth analysis states that a piecewise affine function $F:\mathbb R^n\rightarrow\mathbb R^n$ is surjective if it is coherently oriented in that the linear parts of its selection functions all have the same nonzero…

We prove Veech's conjecture on the equivalence of Sarnak's conjecture on M\"obius orthogonality with a Kolmogorov type property of Furstenberg systems of the M\''obius function. This yields a combinatorial condition on the M\"obius function…

We show that, for each finite algebra A, either it has symmetric term operations of all arities or else some finite algebra in the variety generated by A has two automorphisms without a common fixed point. We also show this two-automorphism…

We show that a function $f : X \to \mathbb R$ defined on a closed uniformly polynomially cuspidal set $X$ in $\mathbb R^n$ is real analytic if and only if $f$ is smooth and all its composites with germs of polynomial curves in $X$ are real…

In this paper, we study arithmetic dynamics in arbitrary characteristic, in particular in positive characteristic. We generalise some basic facts on arithmetic degree and canonical height in positive characteristic. As applications, we…

In this paper we will first introduce the notion of affine structures on a ringed space and then obtain several properties. Affine structures on a ringed space, arising mainly from complex analytical spaces of algebraic schemes over number…

It is argued that for certain meromorphic functions $u:\cal{R}\rightarrow\cal{R}$ and analytic function $ A_1$ and for any integrable function $F$, as long as it converges as a Cauchy Principal Value,, $$\int_{-\infty}^{\infty}A_1(x)F[u(x)]…

In this article we prove that every germ of analytic meromorphic function at $(\mathbb{C}^{2},0)$ is equivalent, under the right composition by a germ of biholomorphism, to a germ of algebraic meromorphic function. An analogous result is…

It is shown that every holomorphic map $f$ from a Runge domain $\Omega$ of an affine algebraic variety $S$ into a projective algebraic manifold $X$ is a uniform limit of Nash algebraic maps $f_\nu$ defined over an exhausting sequence of…

Following and generalizing a construction by Kontsevich, we associate a zeta function to any matrix with entries in a ring of noncommutative Laurent polynomials with integer coefficients. We show that such a zeta function is an algebraic…

Under very general conditions it is shown that if $A$ is a uniform algebra generated by real-analytic functions, then either $A$ consists of all continuous functions or else there exists a disc on which every function in $A$ is holomorphic.…