Double zeta values, double Eisenstein series, and modular forms of level 2

TL;DR

This paper explores the algebraic relations of double zeta values at level 2, introduces corresponding Eisenstein series, and links them to modular forms of the same level, advancing understanding of their interconnected structures.

Contribution

It introduces double Eisenstein series of level 2 satisfying double shuffle relations and connects them to modular forms, providing new insights into their algebraic and analytical properties.

Findings

Double shuffle relations hold for level 2 double zeta values.

Double Eisenstein series of level 2 are constructed and satisfy these relations.

Connections between double Eisenstein series and modular forms of level 2 are established.

Abstract

We study the double shuffle relations satisfied by the double zeta values of level 2, and introduce the double Eisenstein series of level 2 which satisfy the double shuffle relations. We connect the double Eisenstein series to modular forms of level 2.