Related papers: Sum relations for multiple zeta values and connect…

We introduce the concept of a conical zeta value as a geometric generalization of a multiple zeta value in the context of convex cones. The quasi-shuffle and shuffle relations of multiple zeta values are generalized to open cone subdivision…

Multiple zeta functions of Arakawa-Kaneko and Euler-Zagier types are known as generalizations of the Riemann zeta function. In 2018, Kaneko and Tsumura proved that the multiple zeta functions of Arakawa-Kaneko type can be expressed as a…

In this note, we firstly establish an extended Gauss's summation identity. Using this identity, we compute values of a family of $_4F_3$ hypergeometric functions, which generalize the results obtained by Ferretti et al..

The volume of the unit sphere in every dimension is given a new interpretation as a product of special values of the zeta function of $\mathbb{Z}$, akin to volume formulas of Minkowski and Siegel in the theory of arithmetic groups. A…

The derivative of the Riemann zeta function was computed numerically on several large sets of zeros at large heights. Comparisons to known and conjectured asymptotics are presented.

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…

Extended double shuffle relations for multiple zeta values are obtained by the fact that any product of regularized multiple zeta values has two different representations, and the case of two-fold product is considered in general. In this…

Using some transformation formulas of the generalized hypergeometric series $\,_3F_2$, we give another proof of D. Zagier's evaluation formula of the multiple zeta values $\zeta(2,...,2,3,2,...,2)$.

The hyperharmonic numbers h_{n}^{(r)} are defined by means of the classical harmonic numbers. We show that the Euler-type sums with hyperharmonic numbers: {\sigma}(r,m)=\sum_{n=1}^{\infty}((h_{n}^{(r)})/(n^{m})) can be expressed in terms of…

We construct variants of the Riemann zeta function with convenient properties and make conjectures about their dynamics; some of the conjectures are based on an analogy with the dynamical system of zeta. More specifically, we study the…

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 prove a new linear relation for a q-analogue of multiple zeta values. It is a q-extension of the restricted sum formula obtained by Eie, Liaw and Ong for multiple zeta values.

In this paper, we mainly show that generalized hyperharmonic number sums with reciprocal binomial coefficients can be expressed in terms of classical (alternating) Euler sums, zeta values and generalized (alternating) harmonic numbers.

In this paper, we introduce zeta values of rational convex cones, which is a generalization of cyclotomic multiple zeta values. These zeta values have integral expressions. The main theorem asserts that zeta values of cones can be expressed…

We show how to convert the generating series of interpolated multiple zeta values, or multiple $t$ values, with repeating blocks of length 1 into hypergeometric series. Then we invoke creative telescoping on their generating functions, in…

We present a concise method for deriving an explicit formula for $p$-adic multiple zeta values. The formula features a variant of multiple harmonic sums, termed binomial multiple harmonic sums.

We give a parameterized generalization of the sum formula for quadruple zeta values. The generalization has four parameters, and is invariant under a cyclic group of order four. By substituting special values for the parameters, we also…

We derive new infinite series involving Fibonacci numbers and Riemann zeta numbers. The calculations are facilitated by evaluating linear combinations of polygamma functions of the same order at certain arguments.

In this note, we propose two series expansions of the logarithm of the Glaisher-Kinkelin constant. The relations are obtained using expressions of derivatives of the Riemann zeta function, and one of them involves hypergeometric functions.

We prove a variety of explicit formulas relating special values of generalized hypergeometric functions to lattice sums with four indices of summation. These results are related to Boyd's conjectured identities between Mahler measures and…