Related papers: Four types of variant Euler harmonic sums

The Uniform convergence of double Fourier-Legendre series of function of bounded Harmonic variation and bounded partial $\Lambda $-variation are investigated.

We discuss conditions for complete intersections in a toric variety which allow to compute Hodge numbers if the complete intersection is a quasi-smooth complete variety. A preliminary step is the computation of the Euler characteristic of…

Solutions of nonlinear functional equations are generally not expressed as a finite number of combinations and compositions of elementary and known special functions. One of the approaches to study them is, firstly, to find formal solutions…

We study a variant of multiple zeta values of level 2, which forms a subspace of the space of alternating multiple zeta values. This variant, which is regarded as the `shuffle counterpart' of Hoffman's `odd variant', exhibits nice…

The behaviour of periodic points of discrete Euler top is studied. We derive invariant varieties of periodic points explicitly. When the top is axially symmetric they are specified by some particular values of the angular velocity along the…

Using Euler transformation of series we relate values of Hurwitz zeta function at integer and rational values of arguments to certain rapidly converging series where some generalized harmonic numbers appear. The form of these generalized…

Partial zeta functions of algebraic varieties over finite fields generalize the classical zeta function by allowing each variable to be defined over a possibly different extension field of a fixed finite field. Due to this extra variation…

The harmonic numbers and higher-order harmonic numbers appear frequently in several areas which are related to combinatorial identities, many expressions involving special functions in analytic number theory, and analysis of algorithms. The…

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…

We introduce Schur multiple zeta functions which interpolate both the multiple zeta and multiple zeta-star functions of the Euler-Zagier type combinatorially. We first study their basic properties including a region of absolute convergence…

In this paper we will study the p-divisibility of partial sums of multiple zeta value series. In particular we provide some generalizations of the classical Wolstenholme's Theorem.

We introduce Euler summability method for sequences of fuzzy numbers and state a Tauberian theorem concerning Euler summability method, of which proof provides an alternative to that of K. Knopp[\"Uber das Eulersche Summierungsverfahren II,…

We consider partial sums of a weighted Steinhaus random multiplicative function and view this as a model for the Riemann zeta function. We give a description of the tails and high moments of this object. Using these we determine the likely…

We introduce the method of desingularization of multi-variable multiple zeta-functions (of the generalized Euler-Zagier type), under the motivation of finding suitable rigorous meaning of the values of multiple zeta-functions at…

The aim of this paper is to investigate different types of multi-integrals of finite variation and to obtain decomposition results.

By combining classical techniques together with two novel asymptotic identities contained in [FL], we analyse certain single sums of Riemann-zeta type. In addition, we analyse Euler-Zagier double exponential sums for particular values of…

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…

We define and study the interpolated finite multiple harmonic $q$-series. A generating function of the sums of the interpolated finite multiple harmonic $q$-series with fixed weight, depth and $i$-height is computed. Some Ohno-Zagier type…

In this paper, we investigate the Euler sums $$ G_{n+2}(p,q)=\sum_{1\leq k_1<k_2<\cdots<k_{p+1}}\frac1{k_1k_2\cdots k_pk_{p+1}^{n+2}} \sum_{1\leq\ell_1\leq\ell_2\leq\cdots\leq\ell_q\leq k_{p+1}}\frac1{\ell_1\ell_2\cdots\ell_q}. $$ We give…

In this paper, we define extended trigonometric functions via series and employ the method of contour integration to investigate the parity of certain cyclotomic Euler sums and multiple polylogarithm function. We can provide the statement…