Related papers: A remarkable sequence of integers
A method for estimating the merit factors of sequences will be provided. The result is also effective in determining the nonexistence of certain infinite collections of cyclic difference sets and cyclic matrices and associated binary…
Multiple harmonic-like numbers are studied using the generating function approach. A closed form is stated for binomial sums involving these numbers and two additional parameters. Several corollaries and examples are presented which are…
Some finite series of harmonic numbers involving certain reciprocals are evaluated. Products of such reciprocals are expanded in a sum of the individual reciprocals, leading to a computer program. A list of examples is provided.
In this article a complete set of invariants for ordinary quartic curves in characteristic 2 is computed.
Arithmetical properties of a finite group are properties of the group which are defined by its arithmetical parameters such as the order of the group, the element orders and so on. In this paper, we discuss a number of results on…
The aim of the present article is to explore the possibilities of representing positive integers as sums of other positive integers and highlight certain fundamental connections between their multiplicative and additive properties. In…
We examine the convergence properties of sequences of nonnegative real numbers that satisfy a particular class of recursive inequalities, from the perspective of proof theory and computability theory. We first establish a number of results…
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…
In this paper, we obtain formulas for the number of representations of positive integers as sums of arbitrarily many squares (and other polygonal numbers) with a certain natural weighting. The resulting weighted sums give Fourier…
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.
We review the results having the property of maximal transcendentality.
We study the symmetry properties of autonomous integrating factors from an algebraic point of view. The symmetries are delineated for the resulting integrals treated as equations and symmetries of the integrals treated as functions or…
The fundamental properties of biquaternions (complexified quaternions) are presented including several different representations, some of them new, and definitions of fundamental operations such as the scalar and vector parts, conjugates,…
This is a survey of characterizations and relationships between some properties of lattices, particularly the modular, Arguesian, linear, and distributive properties, but also some other related properties. The survey emphasizes finite and…
The study of combinatorial properties of mathematical objects is a very important research field and continued fractions have been deeply studied in this sense. However, multidimensional continued fractions, which are a generalization…
We characterize the generating function of the number of representations described in the title in terms of the theory of modular forms. Appealing to this characterization we obtain explicit formulas for the representation numbers as…
We provide a characterization of the Arf property in both the numerical duplication of a numerical semigroup and in a member of a family of quotients of the Rees algebra studied in arXiv:1403.4200 [math.AC]
In this paper, we study some properties of associated sequences of special polynomials. From the properties of associated sequences of polynomials, we derive some interesting identities of special polynomials.
A discrete map based on the sum of an integer's distinct primes factors and the sum of its other factors is defined and its iteration is studied.
The review of modern study of algebraic, geometric and differential properties of quaternionic (Q) numbers with their applications. Traditional and "tensor" formulation of Q-units with their possible representations are discussed and groups…