Related papers: A transformal transcendence result for algebraic d…
In this paper we prove a basic theorem which says that if f : F_p^n -> [0,1] has the property that ||f^||_(1/3) is not too ``large''(actually, it also holds for quasinorms 1/2-\delta in place of 1/3), and E(f) = p^{-n} sum_m f(m) is not too…
We get three basic results in algebraic dynamics: (1). We give the first algorithm to compute the dynamical degrees to arbitrary precision. (2). We prove that for a family of dominant rational self-maps, the dynamical degrees are lower…
In this paper, we consider rational functions $f$ with some minor restrictions over the finite field $\mathbb{F}_{q^n},$ where $q=p^k$ for some prime $p$ and positive integer $k$. We establish a sufficient condition for the existence of a…
We explore orbits, rational invariant functions, and quotients of the natural actions of connected, not necessarily finite dimensional subgroups of the automorphism groups of irreducible algebraic varieties. The applications of the results…
Let $K$ be a number field or a function field of characteristic 0. If $K$ is a number field, assume the $abc$-conjecture for $K$. We prove a variant of Zsigmondy's theorem for ramified primes in preimage fields of rational functions in…
Algebraic effects are computational effects that can be described with a set of basic operations and equations between them. As many interesting effect handlers do not respect these equations, most approaches assume a trivial theory,…
In this paper we introduce a particular semigroup transform $\mathcal{A}$ that fixes the invariants involved in Wilf's conjecture, except the embedding dimension. It also allows one to arrange the set of not ordinary and not irreducible…
Let $s_0,s_1,\dots,s_{m-1}$ be complex numbers and $r_0,\dots,r_{m-1}$ rational integers in the range $0\le r_j\le m-1$. Our first goal is to prove that if an entire function $f$ of sufficiently small exponential type satisfies…
Given a reduced local algebra $T$ over a suitable ring or field $k$ we study the question of whether there are nontrivial algebra surjections $R\to T$ which induce isomorphisms $\Omega_{R/k}\otimes T \to \Omega_{T/k}$. Such maps, called…
Consider the algebraic dynamics on a torus T=G_m^n given by a matrix M in GL_n(Z). Assume that the characteristic polynomial of M is prime to all polynomials X^m-1. We show that any finite equivariant map from another algebraic dynamics…
According to the algebraic approach to spacetime, a thoroughgoing dynamicism, physical fields exist without an underlying manifold. This view is usually implemented by postulating an algebraic structure (e.g., commutative ring) of…
Fourier sine transforms containing irrational integrands are presented. Explicit closed form expressions are shown to be related to Lommel functions and in special cases to the Fresnel integrals. Such integrals arise in the semi-classical…
This paper is concerned with Mahler's method. We study in detail the structure of linear relations between values of Mahler functions at algebraic points. In particular, given a field ${\bf k}$, a Mahler function $f(z)\in{\bf k}\{z\}$, and…
A semigroup $S$ is called an equational domain if any finite union of algebraic sets over $S$ is algebraic. For a finite simple semigroup we find necessary and sufficient conditions to be an equational domain. Moreover, we study semigroups…
Let $S$ be a unital associative ring and $S[t;\sigma,\delta]$ be a skew polynomial ring, where $\sigma$ is an injective endomorphism of $S$ and $\delta$ a left $\sigma$-derivation. For each $f\in S[t;\sigma,\delta]$ of degree $m>1$ with a…
We develop a formalism for performing real space renormalization group transformations of the "decimation type" using perturbation theory. The type of transformations beyond $d=1$ is nontrivial even for free theories. We check the formalism…
We construct the rings of generalized differential operators on the ${\bf h}$-deformed vector space of ${\bf gl}$-type. In contrast to the $q$-deformed vector space, where the ring of differential operators is unique up to an isomorphism,…
An involution $#$ on an associative ring $R$ is \textit{formally real} if a sum of nonzero elements of the form $r^# r$ where $r \in R$ is nonzero. Suppose that $R$ is a central simple algebra (i.e. $R=M_n(D)$ for some integer $n$ and…
In this paper we present a new class of complexity measures, induced by a new data structure for representing $k$-valued functions (operations), called minor decision diagram. The results are presented in terms of Multi-Valued Logic…
Forman's Discrete Morse theory is studied from an algebraic viewpoint. Analogous to independent work of Emil Skoeldberg we show that this theory can be extended to chain complexes of free modules over a ring. We provide three applications…