Related papers: Triangular polynomial maps in characteristic $p$

We make the interprecision transfers explicit in an algorithmic description of iterative refinement and obtain new insights into the algorithm. One example is the classic variant of iterative refinement where the matrix and the…

We study degree preserving maps over the set of irreducible polynomials over a finite field. In particular, we show that every permutation of the set of irreducible polynomials of degree $k$ over $\mathbb{F}_q$ is induced by an action from…

This paper focuses on a numerical invariant for local rings of characteristic $p$ called $h$-function, that recovers several important invariants, including the Hilbert-Kunz multiplicity, $F$-signature, $F$-threshold, and $F$-signature of…

New approach to systems of polynomial recursions is developed based on the Carleman linearization procedure. The article is divided into two main sections: firstly, we focus on the case of uni-variable depth-one polynomial recurrences.…

We consider symbolic flows over finite alphabets and study certain kinds of repetitions in these sequences. Positive and negative results for the existence of such repetitions are given for codings of interval exchange transformations and…

The characterization of permutations over finite fields is an important topic in number theory with a long-standing history. This paper presents a systematic investigation of low-degree bivariate polynomial systems $F=(f_1(x,y),f_2(x,y))$…

A polynomial triangle is an array whose inputs are the coefficients in integral powers of a polynomial. Although polynomial coefficients have appeared in several works, there is no systematic treatise on this topic. In this paper we plan to…

Using the diagrammatic approach to integrals over Gaussian random matrices, we find a representation for polynomial Lie group integrals as infinite sums over certain maps on surfaces. The maps involved satisfy a specific condition: they…

It is well known that there is a one-to-one correspondence between supersingular $j$-invariants up to the action of $\text{Gal}(\mathbb{F}_{p^2}/\mathbb{F}_p)$ and type classes of maximal orders in $B_{p,\infty}$ by Deuring's theorem.…

Let $R$ be a commutative, indecomposable ring with identity and $(P,\le)$ a partially ordered set. Let $FI(P)$ denote the finitary incidence algebra of $(P,\le)$ over $R$. We will show that, in most cases, local automorphisms of $FI(P)$ are…

In this paper, with the help of trinomial coefficients we study some arithmetic properties of certain determiants involving reciprocals of binary quadratic forms over finite fields.

In this paper we present an iterative construction of irreducible polynomials over finite fields based upon repeated applications of transforms induced by endomorphisms of odd prime degree of ordinary elliptic curves.

By using the piecewise method, Lagrange interpolation formula and Lucas' theorem, we determine explicit expressions of the inverses of a class of reversed Dickson permutation polynomials and some classes of generalized cyclotomic mapping…

Every classical orthogonal polynomial system $p_n(x)$ satisfies a three-term recurrence relation of the type \[ p_{n+1}(x)=(A_nx+B_n)p_n(x)-C_np_{n-1}(x)~ (n=0,1,2,\ldots, p_{-1}\equiv 0), \] with $C_nA_nA_{n-1}>0$. Moreover, Favard's…

In this paper, we propose a new and simple approach to the approximation algorithms that are modified and improved from our published results. The computational and graphical examples are presented with the aid of Maple procedures.

Using the recent proof of the polynomial Freiman-Ruzsa conjecture over $\mathbb{F}_p^n$ by Gowers, Green, Manners, and Tao, we prove a version of the polynomial Freiman-Ruzsa conjecture over function fields. In particular, we prove that if…

For any algebraically closed field $K$ and any endomorphism $f$ of $\mathbb{P}^1(K)$ of degree at least 2, the automorphisms of $f$ are the M\"obius transformations that commute with $f$, and these form a finite subgroup of…

We prove the global triangulation conjecture for families of refined p-adic representations under a mild condition. That is, for a refined family, the associated family of (phi, Gamma)-modules admits a global triangulation on a Zariski open…

This paper continues our investigation of the dynamics of families of transcendental meromorphic functions with finitely many singular values all of which are finite. Here we look at a generalization of the family of polynomials…

We give a new proof of Fitzgerald's criterion for primitive polynomials over a finite field. Existing proofs essentially use the theory of linear recurrences over finite fields. Here, we give a much shorter and self-contained proof which…