Zeta elements in depth 3 and the fundamental Lie algebra of a punctured elliptic curve

Abstract

This paper draws connections between the double shuffle equations and structure of associators; universal mixed elliptic motives as defined by Hain and Matsumoto; and the Rankin-Selberg method for modular forms for $S{L}_2(\mathbb{Z})$. We write down explicit formulae for zeta elements ${\sigma }_{2n-1}$ (generators of the Tannaka Lie algebra of the category of mixed Tate motives over $\mathbb{Z}$) in depths up to four, give applications to the Broadhurst-Kreimer conjecture, and completely solve the double shuffle equations for multiple zeta values in depths two and three.

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Cited by in corpus (8)

• Elliptic multiple zeta values, Grothendieck-Teichmüller and mould theory
• Relationships between multiple zeta values of depths 2 and 3 and period polynomials
• On linear relations among totally odd multiple zeta values related to period polynomials
• Anatomy of an associator
• Moduli of framed formal curves
• Multiple Landen values and the tribonacci numbers
• Motivic Multiple Zeta Values and the Block Filtration
• On triple zeta values of even weight and their connections with period polynomials