相关论文: A Skolem-Mahler-Lech Theorem in Positive Character…

J.~Rosen introduced the ring $\mathcal{P}^0_{\mathcal{A}}$ of so-called finite algebraic numbers, which may be seen as an analogue of certain periods in the ring $\mathcal{A}=\prod_p \mathbb{Z}/p\mathbb{Z} /\bigoplus_p…

We discuss here characteristic $p$ $L$-series as well as the group $S_{(q)}$ which appears to act as symmetries of these functions. We explain various actions of $S_{(q)}$ that arise naturally in the theory as well as extensions of these…

Building off of recent results on Keisler's order, we show that consistently, $\leq_{SP}$ has infinitely many classes. In particular, we define the property of $\leq k$-type amalgamation for simple theories, for each $2 \leq k < \omega$. If…

Stanley proved that, in characteristic zero, all artinian monomial complete intersections have the strong Lefschetz property. We provide a positive characteristic complement to Stanley's result in the case of artinian monomial complete…

By generalizing the classical Selberg-Chowla formula, we establish the analytic continuation and functional equation for a large class of Epstein zeta functions. This continuation is studied in order to provide new classes of theorems…

We prove that any quadratic complete intersection with certain action of the symmetric group has the strong Lefschetz property over a field of characteristic zero. As a consequence of it we construct a new class of homogeneous complete…

Kleisli categories have long been recognised as a setting for modelling the linear behaviour of various types of systems. However, the final coalgebra in such settings does not, in general, correspond to a fixed notion of linear semantics.…

V. I. Arnold proved in 1991 (published in 1993) that the intersection multiplicity between two germs of analytic subvarieties at a fixed point of a holomorphic invertible self-map remains bounded when one of the germs is dragged by…

Linear Dynamical Systems, both discrete and continuous, are invaluable mathematical models in a plethora of applications such the verification of probabilistic systems, model checking, computational biology, cyber-physical systems, and…

We prove, in ZFC, that there is an infinite strictly descending chain of classes of theories in Keisler's order. Thus Keisler's order is infinite and not a well order. Moreover, this chain occurs within the simple unstable theories,…

We show that finite-dimensional Lie algebras over a field of characteristic zero such that their high-degree cohomology in any finite-dimensional non-trivial irreducible module vanishes, are, essentially, direct sums of semisimple and…

For any irreducible character $\chi$ of a finite group $G$, let $\theta(\chi)$ denote the proportion of elements $g\in G$ for which $\chi(g)$ is either zero or a root of unity. Then for any $L\in[1/2,1]$ and any $\epsilon>0$, there exists…

This paper investigates the class of finitely presented monoids defined by homogeneous (length-preserving) relations from a computational perspective. The properties of admitting a finite complete rewriting system, having finite derivation…

Basic properties of symplectic reflection algebras over an algebraically closed field k of positive characteristic are laid out. These algebras are always finite modules over their centres, in contrast to the situation in characteristic 0.…

A zero-sum sequence over ${\mathbb Z}$ is a sequence with terms in ${\mathbb Z}$ that sum to $0$. It is called minimal if it does not contain a proper zero-sum subsequence. Consider a minimal zero-sum sequence over ${\mathbb Z}$ with…

We develop a theory of linear Mahler systems in several variables from the perspective of transcendence and algebraic independence, which also includes the possibility of dealing with several systems associated with sufficiently independent…

Let f(x_1,x_2,...,x_m) = u_1x_1+u_2 x_2+... + u_mx_m be a linear form with positive integer coefficients, and let N_f(k) = min{|f(A)| : A \subseteq Z and |A|=k}. A minimizing k-set for f is a set A such that |A|=k and |f(A)| = N_f(k). A…

Let $a=(a_n)_{n\ge 1}$ be a periodic sequence, $F_a(s)$ the meromorphic continuation of $\sum_{n\ge 1} a_n/n^s$, and $N_a(\sigma_1, \sigma_2, T)$ the number of zeros of $F_a(s)$, counted with their multiplicities, in the rectangle $\sigma_1…

It is well known that ZFC, despite its usefulness as a foundational theory for mathematics, has two unwanted features: it cannot be written down explicitly due to its infinitely many axioms, and it has a countable model due to the…

We provide a sufficient condition that ensures the nilpotency of endomorphisms universally of trace zero of Schur-finite objects in a category of homological type, i.e., a Q-linear tensor category with a tensor functor to super vector…