Related papers: Dualities for absolute zeta functions and multiple…

We consider a variant expression to regularize the Euler product representation of the zeta functions, where we mainly apply to that of the Riemann zeta function in this paper. The regularization itself is identical to that of the zeta…

The aim of this work is to study the analytic continuation of the doubly-periodic Barnes zeta function. By using a suitable complex integral representation as a starting point we find the meromorphic extension of the doubly periodic Barnes…

For a general ${\cal N}=1$ supersymmetric gauge theory regularized by higher covariant derivatives we prove in all orders that the $\beta$-function defined in terms of the bare couplings is given by integrals of double total derivatives…

In the paper, the author expresses the difference $2^m\bigl[\zeta\bigl(-m,\frac{1+x}{2}\bigr)-\zeta\bigl(-m,\frac{2+x}{2}\bigr)\bigr]$ in terms of a linear combination of the function $\Gamma(m+1){\,}_2F_1(-m,-x;1;2)$ for $m\in\mathbb{N}_0$…

As well known, the study of Riemanns zeta function {\zeta}(s) involves the related entire function {\xi}(s). A close relative of {\zeta}(s) is the alternating zeta function {\eta}(s). Similar to {\zeta}(s), also {\eta}(s) has a…

In this paper we discuss three types of the mean values of the Euler double zeta function. In order to get results we introduce three approximate formulas for this function.

Let $X$ be a smooth proper curve over a finite field and let $\infty \in X$ be a closed point. Let $A$ be the ring of functions on $X - \infty$. The Goss zeta function $\zeta_A$ of $A$ is an equicharacteristic analogue of the Riemann zeta…

We compute explicitly the normal zeta functions of the Heisenberg groups $H(R)$, where $R$ is a compact discrete valuation ring of characteristic zero. These zeta functions occur as Euler factors of normal zeta functions of Heisenberg…

This article deals with applications of Voronin's universality theorem for the Riemann zeta-function $\zeta$. Among other results we prove that every plane smooth curve appears up to a small error in the curve generated by the values…

In recent work where Matsusaka generalizes the relationship between Habiro-type series and false theta functions after Hikami, five families of Hecke-type double-sums of the form \begin{equation*} \left( \sum_{r,s\ge 0…

For $\alpha\geq 0$, $\delta>0$, $\beta<1$ and $\gamma\geq 0$, the class $\mathcal{W}_{\beta}^\delta(\alpha,\gamma)$ consist of analytic and normalized functions $f$ along with the condition \begin{align*} {\rm Re\,}…

In the following work, we first propose two (partial summation) formulas involving the floor and ceiling functions. We use principle of mathematical induction to prove the propositions. Another formula relating to the difference of floor…

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 present the beta functions of gauge and Yukawa couplings in general four-dimensional quantum field theory, at four and three loops, respectively. The essence of our approach is fixing unknown coefficients in the most general ansatz for…

We introduce the multiple zeta functions with structures similar to those of symmetric functions such as Schur $P$-, Schur $Q$-, symplectic and orthogonal functions in the representation theory. We first consider their basic properties such…

In this paper, we give Hurwitz-Lerch zeta distributions with $0 < \sigma \ne 1$ by using the Gamma function. Moreover, we define Hurwitz-Lerch type of Euler-Zagier double zeta distributions not only in the region of absolute convergence but…

In this paper, the problem of multiplicative anomaly of zeta regularization is solved for polynomials. For a regularizable sequence $\Lambda$, we explicitly calculate the zeta regularized product of $(\Lambda-z_1)\dots(\Lambda-z_n)$ for…

A general algebraic method of quantum corrections evaluations is presented. Quantum corrections to a few classical solutions of Landau-Ginzburg model (phi-in-quadro) are calculated in arbitrary dimensions. The Green function for heat…

We produce explicit formulae for various ideal zeta functions associated to the members of an infinite family of class-$2$-nilpotent Lie rings, introduced in [1], in terms of Igusa functions. As corollaries we obtain information about…

For $0\neq x>-1$ let $$\Delta(x)={{\ln \Gamma(x+1)} \over x}.$$ Recently Adell and Alzer proved the complete monotonicity of $\Delta'$ on $(-1,\infty)$ by giving an integral representation of $(-1)^n \Delta^{(n+1)}(x)$ in terms of the…