Related papers: On an arithmetic convolution

We consider here a particular quadratic equation linking two elements of a C-Algebra. By analysing powers of the unknowns, it appears a double sequence of polynomials related to classical Bernoulli polynomials. We get the generating…

The aim of this paper is to study a dimorphic property associated with two different sums of identically independent Bernoulli random variables having two different families of probability mass functions. In addition, we give two…

Euler's gamma function is logarithmically convex on positive semi-axis. Additivity of logarithmic convexity implies that the function sum of gammas with non-negative coefficients is also log-convex. In this paper we investigate the series…

Given two arithmetical functions $f,g$ we derive, under suitable conditions, asymptotic formulas with error term, for the convolution sums $\sum_{n \le N} f(n) g(n+h)$, building on an earlier work of Gadiyar, Murty and Padma. A key role in…

We show variants of the genus inequality for the irreducible components of the special fiber of an arithmetic curve over a henselian discrete valuation ring of residue characteristic zero that take into account the non-existence of…

We consider a functional $\mathcal F$ on the space of convex bodies in $\R^n$ defined as follows: ${\mathcal F}(K)$ is the integral over the unit sphere of a fixed continuous functions $f$ with respect to the area measure of the convex body…

Using duality and topological theory of well behaved Hopf algebras (as defined in [2]) we construct star-product models of non compact quantum groups from Drinfeld and Reshetikhin standard deformations of enveloping Hopf algebras of simple…

By using the Newton interpolation formula, we generalize the recent identities on the Catalan triangle obtained by Miana and Romero as well as those of Chen and Chu. We further study divisibility properties of sums of products of binomial…

In this paper we study the following type of functions $f: \mathcal{Q}_{\mathbb{R}_{3}} \to \mathbb{R}_{3}$, where $ \mathcal{Q}_{\mathbb{R}_3}$ is the quadratic cone of the algebra $\mathbb{R}_{3}$. From the fact that it is possible to…

We generalize a theorem of Bellow and Calder\'on concerning the a.e. convergence of the convolution powers $\ds \mu^nf(x)=\sum_{k}\mu^n(k)f(T^k x)$ where $T$ is a measure preserving transformation of a probability space and $\mu$ is a…

The usual product $m\cdot n$ on $\mathbb{Z}$ can be viewed as the sum of $n$ terms of an arithmetic progression whose first term is $a_{1}=m-n+1$ and whose difference is $d=2$. Generalizing this idea, we define new similar product mappings,…

We show that a pair of newforms $(f,g)$ can be uniquely determined by the product of the central $L$-values of their twists. To achieve our goal, we prove an asymptotic formula for the average of the product of the central values of two…

The two variable Kostka functions are the scalar products of the Macdonald polynomials with the Schur polynomials with respect to the scalar product which makes the Hall-Littlewood polynomials pairwise orthogonal. A conjecture of Macdonald…

Polynomial functions $f : \mathbb{N}_+ \longrightarrow \mathbb{N}_+$ are studied for which sums of arbitrary length $f (1) + f (2) + f (3) + >... + f (n)$, with $n \in \mathbb{N}_+$, can be expressed by polynomial functions $g :…

Motivated by the convolutive behavior of the counting function for partitions with designated summands in which all parts are odd, we consider coefficient sequences $(a_n)_{n\ge 0}$ of primitive eta-products that satisfy the generic…

For a connected real Lie group $G$ we consider the canonical standard-ordered star product arising from the canonical global symbol calculus based on the half-commutator connection of $G$. This star product trivially converges on polynomial…

In this paper, we study the mean value distributions of Dirichlet $L$-functions at positive integers. We give some explicit formulas for the mean values of products of two and three Dirichlet $L$-functions at positive integers weighted by…

Properties of the shuffle product suggest the definition of a quadratic form with domain and values in formal power series over a field of characteristic 2. This quadratic form preserves rational (respectively algebraic) power series and…

Let $m$, $r$ and $n$ be positive integers. We denote by ${\bf k}\vdash n$ any tuple of odd positive integers ${\bf k}=(k_1,\dots,k_t)$ such that $k_1+\dots+k_t=n$ and $k_j\ge 3$ for all $j$. In this paper we prove that for every…

The functions on a lattice generated by the integer degrees of $q^2$ are considered, 0<q<1. The $q^2$-translation operator is defined. The multiplicators and the $q^2$-convolutors are defined in the functional spaces which are dual with…