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In this work, Miller Ross function with bicomplex arguments has been introduced. Various properties of this function including recurrence relations, integral representations and differential relations are established. Furthermore, the…
In this paper, we introduce and share the new concept of $\mathcal{MT}(\lambda )$-functions and its some characterizations.
This paper discusses the simplest examples of spectral zeta functions, especially those associated with graphs, a subject which has not been much studied. The analogy and the similar structure of these functions, such as their parallel…
By developing a connection between partial theta functions and Appell-Lerch sums, we find and prove a formula which expresses Hecke-type double sums in terms of Appell-Lerch sums and theta functions. Not only does our formula prove…
We study multiple zeta values and their generalizations from the point of view of Rota--Baxter algebras. We obtain a general framework for this purpose and derive relations on multiple zeta values from relations in Rota--Baxter algebras.
In this paper we study the characters of N=3 superconformal modules by using the Zwegers' theory on modification of mock theta functions.
The Legendre type relation for the counting function of ordinary twin primes is reworked in terms of the inverse of the Riemann zeta function. Its analysis sheds light on the distribution of the zeros of the Riemann zeta function in the…
An investigation of two-time correlation functions is reported within the framework of (i) Stochastic Quantum Mechanics and (ii) conventional Heisenberg-Schr\"odinger Quantum Mechanics. The spectral functions associated with the two-time…
Multifractal analysis refers to the study of the local properties of measures and functions, and consists of two parts: the fine multifractal theory and the coarse multifractal theory. The fine and the coarse theory are linked by a web of…
It is shown that novel relations between multiple zeta values and single-variable multiple polylogarithms at 1/2 (delta values) can be derived by comparing two distinct, yet a priori equal, series formulae for the Drinfeld associator (from…
As a continuation of the authors and Wakatsuki's previous paper [5], we study relations among Dirichlet series whose coefficients are class numbers of binary cubic forms. We show that for any integral models of the space of binary cubic…
We develop a practical method for computing local zeta functions of groups, algebras, and modules in fortunate cases. Using our method, we obtain a complete classification of generic local representation zeta functions associated with…
This paper presents a detailed symbolic approach to the study of self-similar tilings. It uses properties of addresses associated with graph-directed iterated function systems to establish conjugacy properties of tiling spaces. Tiles may be…
Identities involving cyclic sums of terms composed from Jacobi elliptic functions evaluated at $p$ equally shifted points were recently found. The purpose of this paper is to re-express these cyclic identities in terms of ratios of Jacobi…
In this paper, we will use the local theta correspondences for the dual pair (Sp(W),O(V)) to investigate some branching law problems.
For a Borel measure on the unit interval and a sequence of scales that tend to zero, we define a one-parameter family of zeta functions called multifractal zeta functions. These functions are a first attempt to associate a zeta function to…
T. Ito defined an analog of the Arakawa-Kaneko zeta function to obtain relations among Mordell-Tornheim multiple zeta values. In this paper, we develop two things related to an analog of the Arakawa-Kaneko zeta function. One is to find an…
In this paper, we study the solutions of the system of bilateral type matrix differential equations and presented these solutions in terms of Lauricella hypergeometric matrix functions of several variables and Srivastava's triple…
We shall define the q-analogs of multiple zeta functions and multiple polylogarithms in this paper and study their properties, based on the work of Kaneko et al. and Schlesinger, respectively.
In this paper, by using the residue theorem and asymptotic formulas of trigonometric and hyperbolic functions at the poles, we establish many relations involving two or more infinite series of trigonometric and hyperbolic trigonometric…