Related papers: Introducing an Analysis in Finite Fields
We give an algorithm to compute the series expansion for the inverse of a given function. The algorithm is extremely easy to implement and gives the first $N$ terms of the series. We show several examples of its application in calculating…
Recently, the authors Khalil, R., Al Horani, M., Yousef. A. and Sababheh, M., in " A new Denition Of Fractional Derivative, J. Comput. Appl. Math. 264. pp. 6570, 2014. " introduced a new simple well-behaved definition of the fractional…
Based on the simple and well understood concept of subfields in a finite field, the technique called `field reduction' has proved to be a very useful and powerful tool in finite geometry. In this paper we elaborate on this technique. Field…
A survey on algorithms for computing discrete logarithms in Jacobians of curves over finite fields.
Class field theory furnishes an intrinsic description of the abelian extensions of a number field that is in many cases not of an immediate algorithmic nature. We outline the algorithms available for the explicit computation of such…
Many complex systems are characterized by intriguing spatio-temporal structures. Their mathematical description relies on the analysis of appropriate correlation functions. Functional integral techniques provide a unifying formalism that…
The aim of this paper is to exhibit a method for proving that certain analytic functions are not solutions of algebraic differential equations. The method is based on model-theoretic properties of differential fields and properties of…
In this paper, a new calculus on sequences is defined. Also, the $\lambda$-derivative and the $\lambda$-integration are investigated. The fundamental theorem of $\lambda$-calculus is included. A suitable function basis for the…
We show that a finite-dimensional tame division algebra D over a Henselian field F has a maximal subfield Galois over F if and only if its residue division algebra has a maximal subfield Galois over the residue field of F. This generalizes…
Jacobson developed a counterpart of Galois theory for purely inseparable field extensions in positive characteristic. In his theory, a certain type of derivations replace the role of the generators of Galois groups. This article provides a…
We consider scalar field theory defined over a direct product of the real and $p$-adic numbers. An adjustable dynamical scaling exponent $z$ enters into the microscopic lagrangian, so that the Gaussian theories provide a line of fixed…
The article is devoted to approximate, global and along curves differentiability of functions over non-archimedean infinite fields with non-trivial valuations. Fields with zero and non-zero characteristics are considered. Spaces of…
We describe several families of permutation polynomials obtained using functions with linear translators.
The classical Ruckert-Lefschetz scheme of analysis of implicit functions (defined by finite systems of n analytical equations with n unknowns) is studied from the point of view of calculations with finite number coefficients in Taylor…
Spherical Bessel functions appear commonly in many areas of physics wherein there is both translation and rotation invariance, and often integrals over products of several arise. Thus, analytic evaluation of such integrals with different…
This paper examines finite field trigonometry as a tool to construct trigonometric digital transforms. In particular, by using properties of the k-cosine function over GF(p), the Finite Field Discrete Cosine Transform (FFDCT) is introduced.…
Counting number fields with prescribed Galois group is an enduring challenge in arithmetic statistics. Using the determinant method, we provide an upper bound for even groups, which is new in some cases.
The notion of a separable extension is an important concept in Galois theory. Traditionally, this concept is introduced using the minimal polynomial and the formal derivative. In this work, we present an alternative approach to this…
In this work, we introduce the new class of functions which can use to solve the nonlinear/linear multi-dimensional differential equations. Based on these functions, a numerical method is provided which is called the Developed Lagrange…
Let us consider a generalized Artin-Schreier algebraic function field extension $F$ of the rational function field $\F_{p^n}(x)$ defined over the finite field extension $K=\F_{p^n}$ of the prime field $\F_p$. We assume that $K$ is…