Related papers: Sun's Series via Cyclotomic Multiple Zeta Values

We give a proof of two identities involving binomial sums at infinity conjectured by Z-W Sun. In order to prove these identities, we use a recently presented method i.e. we view the series as specializations of generating series and derive…

We combine the powerful method of Wilf-Zeilberger pairs with systematic theory of multiple zeta values to prove a large number of series identities due to Z.W. Sun, many of them have been long standing conjectures.

By introducing a generalized notion of multiple zeta values associated with an arbitrary finite subset $S\subset \mathbb{P}^1(\mathbb{C})$ and studying their transformation properties under rational functions, we show that multiple…

In this paper we prove some new identities for multiple zeta values and multiple zeta star values of arbitrary depth by using the methods of integral computations of logarithm function and iterated integral representations of series. By…

We show how infinite series of a certain type involving generalized harmonic numbers can be computed using a knowledge of symmetric functions and multiple zeta values. In particular, we prove and generalize some identities recently…

Binomial coefficients and harmonic numbers are important in many branches of number theory. With the help of the operator method and several summation and transformation formulas for hypergeometric series, we prove eight conjectural series…

In this paper we present many new families of identities for multiple harmonic sums using binomial coefficients. Some of these generalize a few recent results of Hessami Pilehrood et al. As applications we prove several conjectures…

Denote by $\epsilon$ a primitive root of $N^{th}$-unity. In this paper, we show that the unit cyclotomic multiple zeta values for $\mu_N$ generate all the cyclotomic multiple zeta values for $\mu_N$ in cases $N=2,3,4$. Moreover, the unit…

We prove and generalize some recent conjectures of Z.-W. Sun on infinite series whose summands involve products of harmonic numbers and several binomial coefficients. We evaluate various classes of infinite sums in closed form by…

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…

In this paper, we will give another proof of Zhi-Wei Sun's three conjectures on Ap\'{e}ry-like sums involving harmonic numbers by proving some identities among special values of multiple polylogarithms.

The multiple zeta values are generalizations of the values of the Riemann zeta function at positive integers. They are known to satisfy a number of relations, among which are the cyclic sum formula. The cyclic sum formula can be stratified…

In this paper we consider iterated integrals of multiple polylogarithm functions and prove some explicit relations of multiple polylogarithm functions. Then we apply the relations obtained to find numerous formulas of alternating multiple…

We define polynomials of one variable t whose values at t=0 and 1 are the multiple zeta values and the multiple zeta-star values, respectively. We give an application to the two-one conjecture of Ohno-Zudilin, and also prove the cyclic sum…

Multiple zeta values (MZVs, also called Euler sums or multiple harmonic series) are nested generalizations of the classical Riemann zeta function evaluated at integer values. The fact that an integral representation of MZVs obeys a shuffle…

By using the method of iterated integral representations of series, we establish some explicit relationships between multiple zeta values and Integrals of logarithmic functions. As applications of these relations, we show that multiple zeta…

In this paper, we study some Euler-Ap\'ery-type series which involve central binomial coefficients and (generalized) harmonic numbers. In particular, we establish elegant explicit formulas of some series by iterated integrals and…

Harmonic numbers are significant in various branches of number theory. With the help of the digamma function, we prove ten conjectural series of Z.-W. Sun involving harmonic numbers. Several ones of them are also series expansions of…

In this paper we prove a conjecture due to Goncharov and Manin which states that the periods of the moduli spaces $\mathfrak{M}_{0,n}$ of Riemann spheres with $n$ marked points are multiple zeta values. In order to do this, we introduce a…

The Kaneko-Zagier conjecture states that finite and symmetric multiple zeta values satisfy the same relations. In the previous work with H.~Bachmann and Y.~Takeyama, we proved that the finite and symmetric multiple zeta value are obtained…