相关论文: The ubiquitous $\zeta$-function and some of its "u…

We give new integral and series representations of the Hurwitz zeta function. We also provide a closed-form expression of the coefficients of the Laurent expansion of the Hurwitz-zeta function about any point in the complex plane.

In this paper, we investigate meromorphic solutions of certain nonlinear partial differential equations in several complex variables involving differential and functional operators. Let $f$ be a non-constant meromorphic function in…

In this paper we find automorphic functions of coset manifolds with special K\"ahler geometry. We use \zeta-functions to regularize an infinite product over integers which belong to a duality-invariant lattice, this product is known to…

We introduce the zeta function of the prehomogenous vector space of binary cubic forms, twisted by the real analytic Eisenstein series. We prove the meromorphic continuation of this zeta function and identify its poles and their residues.…

This is the first of two papers in which we introduce and study two bivariate zeta functions associated to unipotent group schemes over rings of integers of number fields. One of these zeta functions encodes the numbers of isomorphism…

An odd meromorphic function f(s) is constructed from the Riemann zeta-function evaluated at one-half plus s. The partial fraction expansion, p(s), of f(s) is obtained using the conjunction of the Riemann hypothesis and hypotheses advanced…

We prove a mixed joint discrete universality theorem for a Matsumoto zeta-function $\varphi(s)$ (belonging to the Steuding subclass) and a periodic Hurwitz zeta-function $\zeta(s,\alpha;{\mathfrak{B}})$. For this purpose, certain…

Observing a multiple version of the divisor function we introduce a new zeta function which we call a multiple finite Riemann zeta function. We utilize some $q$-series identity for proving the zeta function has an Euler product and then,…

In this paper we study spectral zeta functions associated to finite and infinite graphs. First we establish a meromorphic continuation of these functions under some general conditions. Then we study special values in the case of standard…

In this paper we define a continuous version of multiple zeta functions. They can be analytically continued to meromorphic functions on $\mathbb{C}^r$ with only simple poles at some special hyperplanes. The evaluations of these functions at…

By using sheaf-theoretical methods such as constructible sheaves, we generalize the formula of Libgober-Sperber concerning the zeta functions of monodromy at infinity of polynomial maps into various directions. In particular, some formulas…

We give an explicit formula of the coefficients of the Zeta-Function's L-polynomial for algebraic function fields over finite constant fields. Thus, we deduce an expression of the class number of algebraic function fields defined over…

In this paper, we obtain the meromorphic continuation of a q-analogue of multiple zeta function using an elementary formula called translation formula. We then obtain the matrix representation of the translation formula and using it, we…

We show the recurrence relations of the Euler-Zagier multiple zeta-function which describes the $r$-fold function with one variable specialized to a non-positive integer as a rational linear combination of $(r-1)$-fold functions, which…

The Mittag-Leffler function plays an important role in Geometric Function Theory, particularly in the study of analytic and meromorphic function classes. Among its various generalizations, the Barnes-Mittag-Leffler function stands out due…

In a recent article we have discussed the connections between averages of powers of Riemann's $\zeta$-function on the critical line, and averages of characteristic polynomials of random matrices. The result for random matrices was shown to…

In this note it is shown that two key results on transcendental singularities for meromorphic functions of finite lower order have refinements which hold under the weaker hypothesis that the logarithmic derivative has finite lower order.

In this paper, we study the uniqueness of the differential-difference of meromorphic functions. We prove the following result: Let $f$ be a nonconstant meromorphic function of $\rho_{2}(f)<1$, let $\eta$ be a non-zero complex number,…

We study Selberg zeta functions $Z(s,\sigma)$ associated to locally homogeneous vector bundles over the unit-sphere bundle of a complete odd-dimensional hyperbolic manifold of finite volume. We assume a certain condition on the fundamental…

The theory of Ihara zeta functions is extended to non-compact arithmetic quotients of Bruhat-Tits trees. This new zeta function turns out to be a rational function, despite the infinite-dimensional setting. In general it has zeros and…