Related papers: The Lerch zeta function as a fractional derivative

This paper gives some results for the logarithm of the Riemann zeta-function and its iterated integrals. We obtain a certain explicit approximation formula for these functions. The formula has some applications, which are related with the…

We prove that the partial zeta function introduced in [9] is a rational function, generalizing Dwork's rationality theorem.

The definition and main properties of the Ihara zeta function for graphs are reviewed, focusing mainly on the case of periodic simple graphs. Moreover, we give a new proof of the associated determinant formula, based on the treatment…

This paper shows the Fermi-Dirac Integrals expressed in terms of Riemann and Hurwitz Zeta functions. This is done by defining an auxiliar function that permits rewrite the Fermi-Dirac integral in terms of simpler and known integrals…

This paper continues a series of investigations on converging representations for the Riemann Zeta function. We generalize some identities which involve Riemann's zeta function, and moreover we give new series and integrals for the zeta…

We derive a simple expression to analytically continue the prime zeta function to the domain $\Re(s)>\frac{1}{2}$ assuming (RH) and taking into account a proper branch cut. We also verify the formula numerically and provide several plots.

In the present manuscript, we study analytic properties of zeta functions defined by partial Euler products.

Several second moment and other integral evaluations for the Riemann zeta function $\zeta(s)$, Hurwitz zeta function $\zeta(s,a)$, and Lerch zeta function $\Phi(z,s,a)$ are presented. Additional corollaries that are obtained include…

A generalization of a well-known relation between the Riemann zeta function $\zeta(s)$ and Bernoulli numbers $B_n$ is obtained. The formula is a new representation of the Riemann zeta function in terms of a nested series of Bernoulli…

A new derivative, called deformable derivative, is introduced here which is equivalent to ordinary derivative in the sense that one implies other. The deformable derivative is defined using limit approach like that of ordinary one but with…

We use a spectral theory perspective to reconsider properties of the Riemann zeta function. In particular, new integral representations are derived and used to present its value at odd positive integers.

I consider the Lerch-Hurwitz or periodic zeta function as covariance function of a periodic continuous-time stationary stochastic process. The function can be parametrized with a continuous index $\nu$ which regulates the continuity and…

An integral formula is developed which applies to an essentially arbitrary function. An application is made to the Riemann zeta function.

In this paper, we introduce the normalized Shintani L-function of several variables by an integral representation and prove its functional equation. The Shintani L-function is a generalization to several variables of the Hurwitz-Lerch zeta…

We have looked at the evaluation of the Riemann Zeta function at odd arguments and have provided a simple formula to approximate the value with exponential convergence. We have compared it with various other formulae present in literature.…

Partial zeta functions of algebraic varieties over finite fields generalize the classical zeta function by allowing each variable to be defined over a possibly different extension field of a fixed finite field. Due to this extra variation…

This is a review of some of the interesting properties of the Riemann Zeta Function.

We consider the second weighted Bartholdi zeta function of a graph $G$, and present weighted versions for the result of Li and Hou's on the partial derivatives of the determinant part in the determinant expression of the Bartholdi zeta…

We show how to obtain infinitely many continued fractions for certain Z-linear combinations of zeta and L values. The methods are completely elementary.

We describe in detail three distinct families of generalized zeta functions built over the (nontrivial) zeros of a rather general arithmetic zeta or L-function, extending the scope of two earlier works that treated the Riemann zeros only.…