Related papers: Discrete restrictions from Laurent monomial system…

In this paper, we would like to propose a fundamental question about a higher dimensional analogue of Dirichlet's unit theorem. We also give a partial answer to the question as an application of the arithmetic Hodge index theorem.

We investigate Newton series for truncated multiple $L$-values and thereby obtain a class of relations for multiple $L$-values. In addition, we give a formulation and a proof of extended derivation relations for multiple $L$-values.

We announce a detailed numerical investigation for some class of difference schemes, which arises from Euler implicit scheme. Such schemes demonstrate unusual behavior and leads to origin of solitons. Applications to some nonlinear problems…

In this article we shows some results about algebra with the group of units having special polynomial identity.

The aim of this paper is to prove the existence of multiple solutions for a family of nonlinear elliptic systems in divergence form coupled with a pointwise gradient constraint: \begin{align*} \left\{ \begin{array}{ll}…

We have determined composition series of a class of induced representations appearing in Moeglin Tadi\'c classification of discrete series. The result is further used to determine composition series of certain representations induced from…

We introduce sub-Eulerian polynomials to count elements of $D_n$ by which a recurrence relation for the Eulerian polynomials of type $D$ is obtained.

Generalizing the work of A. Morra and the authors, we give explicit formulas for the Dirichlet series generating function of $D_{\ell}$-extensions of odd prime degree $\ell$ with given quadratic resolvent. Over the course of our proof, we…

The aim of this article is to investigate the issues of multiplicative inverses and composition in the set of formal Laurent series. We show the lack of general uniqueness of inverses of formal Laurent series; necessary and sufficient…

The purpose of this article is to develop an algebraic approach to the problem of integrable classification of differential-difference equations with one continuous and two discrete variables. As a classification criterion, we put forward…

The problem of representation of elements of weighted space of infinitely differentiable functions on real line by exponential series is considered.

This paper studies the Euler characteristic of a bicategory based on the concept of magnitudes introduced by Leinster. We focus on its invariance with respect to biequivalence and on the product formula for Buckley's fibered bicategories.

Variational calculus on a vector bundle E equipped with a structure of a general algebroid is developed, together with the corresponding analogs of Euler-Lagrange equations. Constrained systems are introduced in the variational and in the…

We correct the proof of Theorem~8 in [\emph{Weak product spaces of Dirichlet series}, Integral Equations Operator Theory \textbf{86} (2016), no.~4, 453--473.]

We present an integral representation formula for a Dirichlet series whose coefficients are the values of the Liouville's arithmetic function.

In this note we investigate the problem of determining elements of the Selberg class from their Dirichlet series coefficients at the primes. We show that this is possible when the degree is one, but in general need an additional weak…

In this paper, we introduce restricted products for families of locally convex spaces and formulate criteria ensuring that mappings into such products are continuous or smooth. As a special case, can define restricted products of weighted…

In this paper, we derive $C^2$ estimates for a class of mixed Hessian type equations with Dirichlet boundary condition, and obtain the existence theorem of admissible solutions for the classical Dirichlet problem of these mixed Hessian type…

In this paper, we introduce the polynomial continued fraction, a close relative of the well-known simple continued fraction expansions which are widely used in number theory and in general. While they may not possess all the intriguing…

In this note, we evaluate a series for $1/\pi$ conjectured by Sun. Our proof uses the Cauchy product and hypergeometric transformations. From this result, we derive two additional analogous series for $1/\pi$ involving polynomials of degree…