相关论文: A survey on the theory of multiple Dirichlet serie…
In this article we study analytic properties of the multiple Dirichlet series associated to additive and Dirichlet characters. For the multiple Dirichlet series associated to additive characters, the meromorphic continuation is established…
In this paper we study the analytic properties of a multiple Dirichlet series associated to the prehomogeneous vector space of binary cubic forms.
We survey the classical results of the Dirichlet Approximation Theorem.
The manuscript reviews Dirichlet Series of important multiplicative arithmetic functions. The aim is to represent these as products and ratios of Riemann zeta-functions, or, if that concise format is not found, to provide the leading…
We survey general properties of multiplicative arithmetic functions of several variables and related convolutions, including the Dirichlet convolution and the unitary convolution. We introduce and investigate a new convolution, called gcd…
We present a survey on recent developments of generalizations of Forelli's analyticity theorem and related pluripotential methods.
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.
This paper presents a number of identities for Dirichlet series and series with Stirling numbers of the first kind. As coefficients for the Dirichlet series we use Cauchy numbers of the first and second kinds, hyperharmonic numbers,…
This paper develops an analytic theory of Dirichlet series in several complex variables which possess sufficiently many functional equations. In the first two sections it is shown how straightforward conjectures about the meromorphic…
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…
We study a Dirichlet series in two variables which counts primitive three-term arithmetic progressions of squares. We show that this multiple Dirichlet series has meromorphic continuation to $\mathbb{C}^2$ and use Tauberian methods to…
We give an axiomatic characterization of multiple Dirichlet series over the function field $\mathbb F_q(T)$, generalizing a set of axioms given by Diaconu and Pasol. The key axiom, relating the coefficients at prime powers to sums of the…
In the first part of this expository paper, we present and discuss the interplay of Dirichlet polynomials in some classical problems of number theory, notably the Lindel\"of Hypothesis. We review some typical properties of their means and…
A multiple Dirichlet series in two variables is constructed as a Mellin transform of a higher order Eisenstein series. It is shown to extend to a meromorphic function and satisfy two independent functional equations.
We construct multiple Dirichlet series in several complex variables whose coefficients involve quadratic residue symbols. The series are shown to have an analytic continuation and satisfy a certain group of functional equations. These are…
We prove that several results in different areas of number theory such as the divergent series, summation of arithmetic functions, uniform distribution modulo one and summation over prime numbers which are currently considered to be…
In this paper, we give criteria for infinitely many sign changes of the coefficients of any Dirichlet series if the coefficients are real numbers. We also provide examples where our criteria are applicable.
A method of estimating sums of multiplicative functions braided with Dirichlet characters is demonstrated, leading to a taxonomy of the characters for which such sums are large.
The main purpose of this survey is to introduce an inexperienced reader to additive prime number theory and some related branches of analytic number theory. We state the main problems in the field, sketch their history and the basic…
We present an integral representation formula for a Dirichlet series whose coefficients are the values of the Liouville's arithmetic function.