Related papers: An Appell series over finite fields
We have discovered three non-power infinite series representations for Bessel functions of the first kind of integer orders and real arguments. These series contain only elementary functions and are remarkably simple. Each series was…
We study restriction problem in vector spaces over finite fields. We obtain finite field analogue of Mockenhaupt-Mitsis-Bak-Seenger restriction theorem, and we show that the range of the exponentials is sharp.
We prove the finite generation of the adjoint ring for $\mathbb{Q}$-factorial log surfaces over any algebraically closed field.
This is a compendium of generating functions involving single, double sums and definite integrals. These generating functions also involve special functions in both the summand function and closed form solution.
Inspired by the works of L. Carlitz and Z.-W. Sun on cyclotomic matrices, in this paper, we investigate certain cyclotomic matrices involving Gauss sums over finite fields, which can be viewed as finite field analogues of certain matrices…
We give a generating function for the number of unimodal permutations with a given cycle structure.
Cyclic codes over finite fields are widely implemented in data storage systems, communication systems, and consumer electronics, as they have very efficient encoding and decoding algorithms. They are also important in theory, as they are…
We propose a differential analog of the notion of integral closure of algebraic function fields. We present an algorithm for computing the integral closure of the algebra defined by a linear differential operator. Our algorithm is a direct…
The quantum correlations of scalar fields are examined as a power series in derivatives. Recursive algebraic equations are derived and determine the amplitudes; all loop integrations are performed. This recursion contains the same…
The complexity of large-scale distributed systems, particularly when deployed in physical space, calls for new mechanisms to address composability and reusability of collective adaptive behaviour. Computational fields have been proposed as…
We put forward a new method of constructing the complete ordered field of real numbers from the ordered field of rational numbers. Our method is a generalization of that of A. Knopfmacher and J. Knopfmacher. Our result implies that there…
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.
The article presents several methods for the arithmetic of finite abelian groups. We introduce a tool - already used by Delsarte in [1] as I found out later - analogous to Dirichlet's convolution to obtain combinatorial results on these…
In this paper, a method for constructing a near optimal normal basis for algebraic extensions of a finite field is described. In each extension, except for the squares of basis elements, the product of two distinct normal basis elements can…
The interpretation of the optical Appell transformation, as previously elaborated in relation to the free-space paraxial propagation under both a rectangular and a circular cylindrical symmetry, is reviewed. Then, the caloric Appell…
The aim of this paper is to give some combinatorial relations linked polynomials generalizing those of Appell type to the partial r-Bell polynomials. We give an inverse relation, recurrence relations involving some family of polynomials and…
This paper deals with a new kind of generalized functions, called "ultrafunctions" which have been introduced recently and developed in some previous works. Their peculiarity is that they are based on a Non-Archimedean field namely on a…
We prove a new formula for the generating function of polynomials counting absolutely stable representations of quivers over finite fields. The case of irreducible representations is studied in more detail.
Let $\Lambda$ be a finite dimensional algebra over an algebraically closed field $k$. We survey some results on algebras of finite global dimension and address some open problems.
Several structural properties of a universal algebra can be seen from the higher commutators of its congruences. Even on a finite algebra, the sequence of higher commutator operations is an infinite object. In the present paper, we exhibit…