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arXiv · 1504.04737

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

Francis Brown
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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 $SL_2(\mathbb{Z})$. 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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Francis Brown. 2015-04-18. Zeta elements in depth 3 and the fundamental Lie algebra of a punctured elliptic curve. https://arxiv.org/abs/1504.04737

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