Related papers: Unramified Euler sums and Hoffman $\star$ basis

In this paper, we give an elementary account into Zagier's formula for multiple zeta values involving Hoffman elements. Our approach allows us to obtain direct proof in a special case via rational zeta series involving the coefficient…

Flajolet and Salvy pointed out that every Euler sum is a $\mathbb{Q}$-linear combination of multiple zeta values. However, in the literature, there is no formula completely revealing this relation. In this paper, using permutations and…

We prove that the category of mixed Tate motives over $\Z$ is spanned by the motivic fundamental group of $\Pro^1$ minus three points. We prove a conjecture by M. Hoffman which states that every multiple zeta value is a $\Q$-linear…

We give thirty-two diverse proofs of a small mathematical gem--the fundamental Euler sum identity zeta(2,1)=zeta(3) =8zeta(\bar 2,1). We also discuss various generalizations for multiple harmonic (Euler) sums and some of their many…

An identity involving symmetric sums of regularized multiple zeta-star values of harmonic type was proved by Hoffman. In this paper, we prove an identity of shuffle type. We use Bell polynomials appearing in the study of set partitions to…

We give an evaluation for the stuffle-regularised $t^{\ast,V}(\{2\}^a,1,\{2\}^b)$ as a polynomial in single-zeta values, $\log(2)$ and $V$. We then apply this to establish some linear independence results of certain sets of motivic multiple…

We recall a proof of Euler's identity $\sum_{n=1}^{\infty} \frac{1}{n^2}=\frac{\pi^2}{6}$ involving the evaluation of a double integral. We extend the method to find Hurwitz Zeta series of the form $S(k,a)=\sum_{n \in \mathbb{Z}}…

Let $v$ be a finite place of $\mathbb{F}_q(\theta)$. In this paper, we interpret $v$-adic arithmetic gamma values in terms of the $v$-adic crystalline-de Rham periods of Carlitz motives with Complex Multiplication, and establish an…

The explicit formulas expressing harmonic sums via alternating Euler sums (colored multiple zeta values) are given, and some explicit evaluations are given as applications.

In 2008, Muneta found explicit evaluation of the multiple zeta star value $\zeta^\star(\{3, 1\}^d)$, and in 2013, Yamamoto proved a sum formula for multiple zeta star values on 3-2-1 indices. In this paper, we provide another way of…

We aim to investigate the four types of variant Euler harmonic sums. Also, as corollaries, we provide particular examples of our core findings, some of whose further instances are evaluated in terms of basic and well-known functions as well…

We give all possible holomorphic Eisenstein series on $\Gamma_0(p)$, of rational weights greater than $2$, and with multiplier systems the same as certain rational-weight eta-quotients at all cusps. We prove they are modular forms and give…

We give a natural construction of unramified over Z framed mixed Tate motives, whose periods are the multiple zeta values. Namely, for each convergent multiple zeta-value we define two boundary divisors A and B in the moduli space M_{0,n+3}…

In this paper, we will define analogues of multiple zeta values by replacing the differential forms defining multiple zeta values with some $\mathbb{Q}$-rational differential forms on the Fermat curve $F_2$ of degree 2 and discuss their…

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…

We define a family {$\gamma(P)$} of generalized Euler constants indexed by finite sets of primes $P$ and study their distribution. These arise from partial sums of reciprocals of integers not divisible by any prime in $P$. An apparent…

We define the generalized-Euler-constant function $\gamma(z)=\sum_{n=1}^{\infty} z^{n-1} (\frac{1}{n}-\log \frac{n+1}{n})$ when $|z|\leq 1$. Its values include both Euler's constant $\gamma=\gamma(1)$ and the "alternating Euler constant"…

Extending Eulerian polynomials and Faulhaber's formula 1, we study several combi-natorial aspects of harmonic sums and polylogarithms at non-positive multi-indices as well as their structure. Our techniques are based on the combinatorics of…

Let $\gamma$ be a non-degenerate Ustilovsky geodesic in $Ham (M, \omega)$ generated by $H$. We give a simple proof of a generalization of the conjecture stated in \cite{virtmorse}, relating the Morse index of $ \gamma$, as a critical point…

In this shortnote, a series expansion technique introduced recently by Dancs and He for generating Euler-type formulae for odd zeta values $\:\zeta{(2 k +1)}$, $\zeta{(s)}$ being the Riemann zeta function and $k$ a positive integer, is…