Related papers: From Basel Problem to multiple zeta values

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 give an explicit formula for the well-known parity result for multiple zeta values as an application of the multitangent functions.

We obtain a weighted sum formula of the zeta values at even arguments, and a weighted sum formula of the multiple zeta values with even arguments and its zeta-star analogue. The weight coefficients are given by (symmetric) polynomials of…

Multiple q-zeta values are a 1-parameter generalization (in fact, a q-analog) of the multiple harmonic sums commonly referred to as multiple zeta values. These latter are obtained from the multiple q-zeta values in the limit as q tends to…

We define certain higher-dimensional Dedekind sums that generalize the classical Dedekind-Rademacher sums, and show how to compute them effectively using a generalization of the continued-fraction algorithm. We present two applications.…

The algebraic and combinatorial theory of shuffles, introduced by Chen and Ree, is further developed and applied to the study of multiple zeta values. In particular, we establish evaluations for certain sums of cyclically generated multiple…

Multiple binomial sums form a large class of multi-indexed sequences, closed under partial summation, which contains most of the sequences obtained by multiple summation of products of binomial coefficients and also all the sequences with…

The algebra of big zeta values we introduce in this paper is an intermediate object between multiple zeta values and periods of the multiple zeta motive. It consists of number series generalizing multiple zeta values, the simplest examples,…

We present a summary of recent and older results on Bessel integrals and their relation with zeta numbers.

In this work we introduce a new polynomial representation of the Bernoulli numbers in terms of polynomial sums allowing on the one hand a more detailed understanding of their mathematical structure and on the other hand provides a…

There exists an infinite series of ratios by which one can derive the Riemann zeta function $\zeta(s)$ from Catalan numbers and central binomial coefficients which appear in the terms of the series. While admittedly the derivation is not…

We use visible point vector identities to examine polylogarithms in the neighbourhood of the Riemann zeta function zeroes. New formulas limiting to the trivial zeroes and to the critical line on the zeta function are given. Similar results…

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,…

We consider finite iterated generalized harmonic sums weighted by the binomial $\binom{2k}{k}$ in numerators and denominators. A large class of these functions emerges in the calculation of massive Feynman diagrams with local operator…

We construct and study a certain zeta function which interpolates multi-poly-Bernoulli numbers at non-positive integers and whose values at positive integers are linear combinations of multiple zeta values. This function can be regarded as…

In this series of seven papers, predominantly by means of elementary analysis, we establish a number of identities related to the Riemann zeta function. Whilst this paper is mainly expository, some of the formulae reported in it are…

We prove that every multiple zeta value is a $\mathbb{Z}$-linear combination of $\zeta(k_1,\dots, k_r)$ where $k_i\geq 2$. Our proof also yields an explicit algorithm for such an expansion. The key ingredient is to introduce modified…

In the former part of this paper, we give functional equations for Barnes multiple zeta-functions and consider some relevant results. In particular, we show that Ramanujan's classical formula for the Riemann zeta values can be derived from…

We consider a cyclic analogue of multiple zeta values (CMZVs), which has two kinds of expressions; series and integral expression. We prove an `integral$=$series' type identity for CMZVs. By using this identity, we construct two classes of…

We consider several families of binomial sum identities whose definition involves the absolute value function. In particular, we consider centered double sums of the form \[S_{\alpha,\beta}(n) :=…