相关论文: A multiple sum involving the Moebius function

In this paper we give a systematized treatment to some coincidence situations for multiple summing multilinear mappings which extend, generalize and simplify the methods and results obtained thus far. The application of our general results…

In studying the complexity of iterative processes it is usually assumed that the arithmetic operations of addition, multiplication, and division can be performed in certain constant times. This assumption is invalid if the precision…

Windowed recurrences are sliding window calculations where a function is applied iteratively across the window of data, and are ubiquitous throughout the natural, social, and computational sciences. In this monograph we explore the…

We consider the sum of squares function in the ring $\mathbb{Z}_{n}$. We determine formulae in a number of cases when $n$ is a power of a prime.

We perform certain alternating binomial summations with parameters that occur in the analysis of algorithms. A combination of integral and special function and special number representations is used. The results are sufficiently general to…

By employing certain extended classical summation theorems, several surprising \pi and other formulae are displayed.

An overview of results and problems concerning the asymptotic behaviour for summatory functions of a certain class of additive functions is given. The class of functions in question involves Karamata's regular variation. Some new Abelian…

In the present paper, firstly, we consider the Volterra integral equation of second type for a remainder term in an asymptotic formula of an arithmetic function which satisfies some special conditions and obtained a solution of the…

We consider a renewal-like recursion and prove that the solution is polynomially decaying asymptotically under suitable conditions. We prove similar results for the corresponding integral equation. In both cases coefficients and functions…

The aim of this work is to prove a Tauberian theorem for the Ingham summability method. The Tauberian theorem we prove is then applied to analyze asymptotics of mean values of multiplicative functions on natural numbers.

In this article, we explore a series of elementary yet insightful results involving integrals related to Gaussian sums. Using techniques rooted in classical calculus, we derive several identities and evaluate nontrivial definite integrals…

We study rather general multiple zeta-functions whose denominators are given by polynomials. The main aim is to prove explicit formulas for the values of those multiple zeta-functions at non-positive integer points. We first treat the case…

We derive various weighted summation identities, including binomial and double binomial identities, for Tribonacci numbers. Our results contain some previously known results as special cases.

Positive definite forms $f$ which are sums of squares are constructed to have the additional property that the members of any collection of forms whose squares sum to $f$ must share a nontrivial complex root.

We introduce a weighted sum of irreducible character ratios as an estimator for commutator probabilities. The estimator yields Frobenius formula when applied to a regular representation

Most of theoretical physics is based on the mathematics of functions of a real or a complex variable; yet we frequently are drawn to try extending our reach to include quaternions. The non-commutativity of the quaternion algebra poses…

We study the asymptotic behavior of Multiple Meixner polynomials of first and second kind, respectively (see J. Arves\'u et al. J. Comput. Appl. Math., 153, (2003)). We use an algebraic function formulation for the solution of the…

Solution of Monge equation of arbitrary degree (non linear differential equation n-orden) is connected with solution of functional equation for 4 functions with 4 different arguments. Some number solutions of this equation is represented in…

In the paper, the author presents a double inequality for completely monotonic degree of a remainder for an asymptotic expansion of the trigamma function. This result partially confirms one in a series of conjectures on completely monotonic…

Asymptotic properties of certain arithmetic functions involving exponential divisors are investigated.