Geodesic
ZETA ELEMENTS IN DEPTH 3 AND THE FUNDAMENTAL LIE ALGEBRA OF THE INFINITESIMAL TATE CURVE
Forum of Mathematics, Sigma, Tome 5 (2017)

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This paper draws connections between the double shuffle equations and structure of associators; Hain and Matsumoto’s universal mixed elliptic motives; and the Rankin–Selberg method for modular forms for $\text{SL}_{2}(\mathbb{Z})$ . We write down explicit formulae for zeta elements $\unicode[STIX]{x1D70E}_{2n-1}$ (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 solve the double shuffle equations for multiple zeta values in depths two and three. 
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     author = {FRANCIS BROWN},
     title = {ZETA {ELEMENTS} {IN} {DEPTH} 3 {AND} {THE} {FUNDAMENTAL} {LIE} {ALGEBRA} {OF} {THE} {INFINITESIMAL} {TATE} {CURVE}},
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FRANCIS BROWN. ZETA ELEMENTS IN DEPTH 3 AND THE FUNDAMENTAL LIE ALGEBRA OF THE INFINITESIMAL TATE CURVE. Forum of Mathematics, Sigma, Tome 5 (2017). doi: 10.1017/fms.2016.29

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