Period polynomial relations between double zeta values

Abstract

The even weight period polynomial relations in the double shuffle Lie algebra $\mathfrak{ds}$ were discovered by Ihara, and completely classified by the second author by relating them to restricted even period polynomials associated to cusp forms on ${\mathrm{SL}}_2(\mathbb{Z})$. In an article published in the same year, Gangl, Kaneko and Zagier displayed certain linear combinations of odd-component double zeta values which are equal to scalar multiples of simple zeta values in even weight, and also related them to restricted even period polynomials. In this paper, we relate the two sets of relations, showing how they can be deduced from each other by duality.

arXiv comment13 pages

Cited by in corpus (10)

• Double Shuffle Relations of Double Zeta Values and Double Eisenstein Series of Level N
• Period polynomial relations between formal double zeta values of odd weight
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• On linear relations among totally odd multiple zeta values related to period polynomials
• Double zeta values, double Eisenstein series, and modular forms of level 2
• On triple zeta values of even weight and their connections with period polynomials
• Depth-graded motivic Lie algebra
• Motivic double zeta values of odd weight
• Modular phenomena for regularized double zeta values