Related papers: Double zeta values, double Eisenstein series, and …

In their seminal paper "Double zeta values and modular forms" Gangl, Kaneko and Zagier defined a double Eisenstein series and used it to study the relations between double zeta values. One of their key ideas is to study the formal double…

We study the $\mthbb{Q}$-vector space generated by the double zeta values with character of conductor $4$. For this purpose, we define associated double Eisenstein series and investigate their relation with modular forms of level $4$.

We study a certain class of q-analogues of multiple zeta values, which appear in the Fourier expansion of multiple Eisenstein series. Studying their algebraic structure and their derivatives we propose conjectured explicit formulas for the…

Bachmann and Tasaka discovered a relationship between multiple Eisenstein series (MES) of level 1 and formal iterated integrals corresponding to multiple zeta value. They also constructed shuffle regularized MES of level 1, which satisfies…

This work is an example driven overview article of recent works on the connection of multiple zeta values, modular forms and q-analogues of multiple zeta values given by multiple Eisenstein series.

In this paper, we introduce the symmetric multiple Eisenstein series, a variant of the multiple Eisenstein series. As a fundamental result, we show that they satisfy the linear shuffle relation. As a case study, we investigate the vector…

We consider the problem of deducing the duality relation from the extended double shuffle relation for multiple zeta values. Especially we prove that the duality relation for double zeta values and that for the sum of multiple zeta values…

In this paper, we study multiple Eisenstein series, which build a natural bridge between the theory of multiple zeta values and modular forms. We prove a large family of relations among these series and propose an explicit conjectural…

This note is a compilation of related research on modular relations for multiple zeta values. Roughly speaking, modular relations are (homogeneous) linear relations of multiple zeta values of fixed weight whose coefficients are `originated'…

In this paper we present some of the recent progresses in multiple zeta values (MZVs). We review the double shuffle relations for convergent MZVs and summarize generalizations of the sum formula and the decomposition formula of Euler for…

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…

We give a proof of double shuffle relations for $p$-adic multiple zeta values by developing higher dimensional version of tangential base points and discussing a relationship with two (and one) variable $p$-adic multiple polylogarithms.

In this paper we consider certain classes of generalized double Eisenstein series by simple differential calculations of trigonometric functions. In particular, we give four new transformation formula for some double Eisenstein series. We…

We construct a family of $q$-series with rational coefficients satisfying a variant of the extended double shuffle equations, which are a lift of a given $\mathbb{Q}$-valued solution of the extended double shuffle equations. These…

In this paper we give two idelic representations of the multiple zeta values - one using iterated integrals over the finite ideles and the other using iterated integrals over the idele class group. Each of the representations leads to a…

This paper contains examples of shuffle relations among multiple Dedekind zeta values. Dedekind zeta values were defined by the author in his paper "Multiple Dedekind zeta functions". Here we concentrate on the cases of real or imaginary…

In this paper, we study the multiple $L$-values and the multiple zeta values of level $N$. We set up the algebraic framework for the double shuffle relations of the multiple zeta values of level $N$. Using the regularized double shuffle…

In this paper, the extended double shuffle relations for interpolated multiple zeta values are established. As an application, Hoffman's relations for interpolated multiple zeta values are proved. Furthermore, a generating function for sums…

We show that the most standard Eisenstein series such as $E_4(\tau)$ or $2E_2(2\tau)-E_2(\tau)$, and also the function $\theta^2(\tau)$, are in a natural way the product of two conjugate Eisenstein series of half their weight and double…

We give an explicit formula for the shuffle relation in a general double shuffle framework that specializes to double shuffle relations of multiple zeta values and multiple polylogarithms. As an application, we generalize the well-known…