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.

References in corpus (3)

• Towards multiple elliptic polylogarithms
• Motivic periods and the projective line minus three points
• On a lower central series filtration of the Grothendieck-Teichmüller Lie algebra grt_1

Cited by in corpus (4)

• Anatomy of an associator
• Multiple Landen values and the tribonacci numbers
• Moduli of framed formal curves
• Motivic Multiple Zeta Values and the Block Filtration