Related papers: Dirichlet series associated to representation numb…

Let k be a quadratic field. We give an explicit formula for the Dirichlet series enumerating cubic fields whose quadratic resolvent field is isomorphic to k. Our work is a sequel to previous work of Cohen and Morra, where such formulas are…

We study the Dirichlet series associated with the integers whose radix-$b$ representation misses certain (fixed) digits. The existence of a meromorphic continuation to the entire complex plane, which was already well-known as a general fact…

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…

Let $k$ be a cubic field. We give an explicit formula for the Dirichlet series $\sum_K|\Disc(K)|^{-s}$, where the sum is over isomorphism classes of all quartic fields whose cubic resolvent field is isomorphic to $k$. Our work is a sequel…

We study Dirichlet series arising as linear functionals on an inner product space of meromorphic functions and establish a relation between the discontinuities of the former on the boundary and the poles and zeros of the latter on the…

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

Assuming a conjecture on distinct zeros of Dirichlet L-functions we get asymptotic results on the average number of representations of an integer as the sum of two primes in arithmetic progression. On the other hand the existence of good…

We study the general theory of weighted Dirichlet series and associated summatory functions of their coefficients. We show that any non-real pole leads to oscillatory error terms. This applies even if there are infinitely many non-real…

We study the Dirichlet series $F_b(s)=\sum_{n=1}^\infty d_b(n)n^{-s}$, where $d_b(n)$ is the sum of the base-$b$ digits of the integer $n$, and $G_b(s)=\sum_{n=1}^\infty S_b(n)n^{-s}$, where $S_b(n)=\sum_{m=1}^{n-1}d_b(m)$ is the summatory…

We characterize the uniform limits of Dirichlet polynomials on a right half plane. In the Dirichlet setting, we find approximation results, with respect to the Euclidean distance and {to} the chordal one as well, analogous to classical…

For an even Dirichlet character psi, we obtain a formula for L(1,psi) in terms of a sum of Dirichlet L-series evaluated at s=2 and s=3 and a rapidly convergent numerical series involving the central binomial coefficients. We then derive a…

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…

In this paper, we show that the regularized determinants of some Dirichlet series are multiplicative. As an application, we give generalizations of Lerch's formula for the classical gamma function and we determine the sum of some Dirichlet…

A representation of SL(2,Z) by integer matrices acting on the space of analytic ordinary Dirichlet series is constructed, in which the standard unipotent element acts as multiplication by the Riemann zeta function. It is then shown that the…

Friedberg, Hoffstein and Lieman have constructed two related multiple Dirichlet series from quadratic and higher-order $L$-functions and Gauss sums. We compute these multiple Dirichlet series explicitly in the case of the rational function…

Some Dirichlet-like functions, attached to a pair (periodic function, polynomial) are introduced and studied. These functions generalize the standard Dirichlet L-functions of Dirichlet characters. They have similar properties, being…

The Dirichlet form is a generalization of the Laplacian, heavily used in the study of many diffusion-like processes. In this paper we present a nonstandard representation theorem for the Dirichlet form, showing that the usual Dirichlet form…

In this article, we obtain the analytic continuation of the multiple shifted Lucas zeta function, multiple Lucas $L$-function associated to Dirichlet characters and additive characters. We then compute a complete list of exact singularities…

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 introduce and study the Dirichlet series enumerating (proper) equivalence classes of full rank subforms/sublattices of a given quadratic form/lattice, focusing on the positive definite binary case. We obtain formulas…