Related papers: Evaluations of multiple Dirichlet $L$-values via s…

The paper explores various special functions which generalize the two-parametric Mittag-Leffler type function of two variables. Integral representations for these functions in different domains of variation of arguments for certain values…

In this paper we investigate the properties of the Euler functions. By using the Fourier transform for the Euler function, we derive the interesting formula related to the infinite series. Finally we give some interesting identities between…

We show that the special values at tuples of positive integers of the $p$-adic multiple $L$-function introduced by the first-named author et al. can be expressed in terms of the cyclotomic multiple harmonic values introduced by the…

We give an expression of polynomials for higher sums of powers of integers via the higher order Bernoulli numbers.

We give three characterizations of the Dirichlet-type spaces $D(\mu)$. First we characterize $D(\mu)$ in terms of a double integral and in terms of the mean oscillation in the Bergman metric, none of them involve the use of derivatives.…

We study several variants of Euler sums by using the methods of contour integration and residue theorem. These variants exhibit nice properties such as closed forms, reduction, etc., like classical Euler sums. In addition, we also define a…

The aim of this paper is to study a dimorphic property associated with two different sums of identically independent Bernoulli random variables having two different families of probability mass functions. In addition, we give two…

In this work we discuss Dirichlet products evaluated at Fibonacci numbers. As first applications of the results we get a representation of Fibonacci numbers in terms of Euler's totient function, an upper bound on the number of primitive…

By using various expansions of the parametric digamma function and the method of residue computations, we study three variants of the linear Euler sums, related Hoffman's double $t$-values and Kaneko-Tsumura's double $T$-values, and…

For each positive integer n, we determine the set of symmetric functions f for which the congruence f(p/1,p/2,...,p/(p-1)) \equiv 0 mod p^n holds for all sufficiently large primes p. Our determination is conditional on a conjecture…

In this paper, we derive some interesting symmetric properties for the geenralized Euler numbers and polynomials.

We consider the value distribution of the difference between logarithms of two symmetric power $L$-functions at $s=\sigma > 1/2$. We prove that certain averages of those values can be written as integrals involving a density function which…

In this paper, we provide an alternative method to calculate the values of generalized multiple Hurwitz zeta function at non-positive integers by means of \emph{Raabe}'s formula and the \textit{Bernoulli} numbers.

In this paper we consider the distribution of large central values of Dirichlet L-functions over cosets of the group of characters modulo q via Soundararajan's resonator method.

We construct an analytic approach to evaluate odd Euler sums, multiple zeta value $\zeta(3,2,\ldots,2)$ and multiple $t$-value $t\left(3,2,\ldots,2\right)$. Moreover, we also conjecture a closed expression for multiple $t$-value…

A variation of multiple $L$-values, which arises from the description of the special values of the spectral zeta function of the non-commutative harmonic oscillator, is introduced. In some special cases, we show that its generating function…

The aim of this paper is to find the numerical solutions of the second order linear and nonlinear differential equations with Dirichlet, Neumann and Robin boundary conditions. We use the Bernoulli polynomials as linear combination to the…

In this paper, we define multi poly-Bernoulli polynomials using multiple polylogarithm and derive some properties parallel to those of poly-Bernoulli polynomials. Furthermore, an explicit formula for certain Hurwitz-Lerch type multi…

First, we define the multiple Dirichlet product and study the properties of it. From those properties, we obtain a zero-free region of a multiple Dirichlet series and a multiple Dirichlet series expression of the reciprocal of a multiple…

The Landau-Selberg-Delange method gives precise asymptotic formulas for the partial sums $\sum_{n \le x} \, a_n$ of a Dirichlet series $\sum_n \, a_n/n^s$ that behaves like a complex power of the Riemann zeta function. However, situations…