Related papers: Analytic properties of Ohno function

In this paper we will focus on the study of relationships that can exist between odd numbers and different traditional functions like the gamma function, Riemann zeta function or function of von Mangoldt. Number theory applies to this…

We introduce a new type of multiple zeta functions, which we call bilateral zeta functions, analogous to the Barnes zeta functions. The bilateral zeta function is a periodic function and shares certain basic properties of Barnes zeta…

We prove a complex interpolation formula for the injective tensor product of vector-valued Banach function spaces satisfying certain geometric assumptions. This result unifies results of Kouba, and moreover, our approach offers an alternate…

We introduce derivations on the algebra of multiple harmonic q-series and show that they generate linear relations among the q-series which contain the derivation relations for a q-analogue of multiple zeta values due to Bradley. As a…

The purpose of this note is to compare various approximation methods as applied to the inverse of the Bessel function of the first kind, in a given domain of the complex plane.

Using twisted Fock spaces, we formulate and study two twisted versions of the n-point correlation functions of Bloch-Okounkov, and then identify them with q-expectation values of certain functions on the set of (odd) strict partitions. We…

Two representations of the Bessel zeta function are investigated. An incomplete representation is constructed using contour integration and an integral representation due to Hawkins is fully evaluated (analytically continued) to produce two…

Using the Quantum Spectral Curve approach we compute exactly an observable (called slope function) in the planar ABJM theory in terms of an unknown interpolating function h(\lambda) which plays the role of the coupling in any integrability…

Given a classical gas described by the truncated correlation functions of all orders, we prove convergence of an expansion of the pair interaction part of the (unknown) potential in terms of the truncated correlation functions of all…

We state and prove a function field analogue of Furusho for multiple zeta values.

We present the real interpolation with variable exponent and we prove the basic properties in analogy to the classical real interpolation. More precisely, we prove that under some additional conditions, this method can be reduced to the…

The problem is addressed of defining the values of functions, whose variables tend to infinity, from the knowledge of these functions at asymptotically small variables close to zero. For this purpose, the extrapolation by means of different…

In this article we study devlop some fundaments for a function theory in the 16-dimensional complexified octonions.

We introduce an analytic function $\Psi(s_1,\ldots,s_r;w)$ that interpolates truncated multiple zeta functions $\zeta_N(s_1,\ldots,s_r)$. We represent this interpolant as a Mellin transform of a function $G(q_1,\ldots,q_r;w)$ and, using…

New recursion relations for the Riemann zeta function are introduced. Their derivation started from the standard functional equation. The new functional equations have both real and imaginary increment versions and can be applied over the…

In this paper, we present the complex interpolation of Besov and Triebel-Lizorkin spaces with generalized smoothness. In some particular cases these function spaces are just weighted Besov and Triebel-Lizorkin spaces. An application, we…

In this paper we develop the analytic theory of a multiple zeta function in d independent complex variables defined over a global function field. This is the function field analog of the Euler-Zagier multiple zeta function of depth d.

This note contains a short proof of the functional equation for the zeta function.

The so called Ahlfors function is the solution to an extremal problem. In this thesis, we study several properties of this function in a most general domain Omega. We consider the Ahlfors function in the context of analytic capacity, and…

In this paper we define and study a Dedekind-like zeta function for the algebra of multicomplex numbers. By using the idempotent representations for such numbers, we are able to identify this zeta function with the one associated to a…