Related papers: Admissible Dirichlet Series

We present other proofs, generalizations and analogues of the identities concerning multiple Dirichlet series by Tahmi and Derbal (2022). As applications, we obtain asymptotic formulas with remainder terms for certain related sums.

In this paper we introduce the notion of admissible skein modules associated to an ideal in a pivotal category. We explain how these modules are generalizations of the Kauffman skein algebra and how they relate to renormalized quantum…

A few years ago, the concept of a D-analogue was introduced as a Dirichlet series analogue for the already known and well researched hypergeometric q-series. The D-analogue of the q-Dixon sum is given here, in the context of seeing a direct…

The category of admissible (in the appropriately modified sense of representation theory of totally disconnected groups) semi-linear representations of the automorphism group of an algebraically closed extension of infinite transcendence…

We give sufficient conditions for a general Dirichlet series to be universal with respect to translations or rearrangements.

We introduce a special class of multiple Dirichlet series whose terms are supported on a variety and which admit an Euler product structure. We proposed several conjectures on the analytic properties of these series.

We present an abstract approach to the abscissas of convergence of vector-valued Dirichlet series. As a consequence we deduce that the abscissas for Hardy spaces of Dirichlet series are all equal. We also introduce and study weak versions…

We introduce subclasses of exact categories in terms of admissible intersections or admissible sums or both at the same time. These categories are recently studied by Br\"ustle, Hassoun, Shah, Tattar and Wegner to give characterisations of…

This paper contains a complete description of classes of the unitary equivalence of the admissible representations of infinite-dimensional classic matrix groups paper.

The Dirichlet divisor problem is used as a model to give a conjecture concerning the conditional convergence of the Dirichlet series of an L-function.

Recently, the concept of a D-analogue was introduced by the author. This is a Dirichlet series analogue for the already known and well researched hypergeometric q-series. we consider the D-analogues of the q-binomial coefficients, and a…

An equivalent formulation of the Riemann hypothesis is given. The physical interpretation of the Riemann hypothesis equivalent formulation is given in the framework of quantum theory terminology. One more power series related to the Riemann…

In this paper, we introduce a novel rule for synthesis of reactive systems, applicable to systems made of n components which have each their own objectives. It is based on the notion of admissible strategies. We compare our novel rule with…

To obtain the Dirichlet series for complex powers of the Riemann zeta function, we define and study the basic properties of a sequence of polynomials that, used as coefficients of the respective terms of the Dirichlet series of the Riemann…

Admissable weight is an important tool for studying spectral invariance in operator algebra. Common admissable weights include polynomial weights and sub exponential weights. This article mainly provides a proof that polynomial weights are…

We generalize the notion of an admissible ideal from path algebras to (small) k-linear categories that satisfy the Krull--Remak--Schmidt--Azumaya assumption. In our treatment we first prove some general results that are analogous to general…

We derive a symplectic analogue of A-directed immersion theorem.

In the present work we show that the Dirichlet series with the Euler product having analytical continuation to the critical strip without singularities, in some natural conditions, can be approximated by partial products of Euler type in…

This paper argues that interpretability research in Artificial Intelligence (AI) is fundamentally ill-posed as existing definitions of interpretability fail to describe how interpretability can be formally tested or designed for. We posit…

In this paper we study the convergence of multiple Dirichlet L-series. In particular we give an integral representation of the series in the region of convergence by using Abel's summation formula. A certain generalized result is also…