Depth-graded motivic multiple zeta values

By F. Brown. Compositio Mathematica, 2013

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We study the depth filtration on multiple zeta values, on the motivic Galois group of mixed Tate motives over $\mathbb {Z}$ and on the Grothendieck–Teichmüller group, and its relation to modular forms. Using period polynomials for cusp forms for $\mathrm {SL} _2(\mathbb {Z})$, we construct an explicit Lie algebra of solutions to the linearized double shuffle equations, which gives a conjectural description of all identities between multiple zeta values modulo $\zeta (2)$ and modulo lower depth. We formulate a single conjecture about the homology of this Lie algebra which implies conjectures due to Broadhurst and Kreimer, Racinet, Zagier, and Drinfeld on the structure of multiple zeta values and on the Grothendieck–Teichmüller Lie algebra.

Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/126af08b2034e8c97a32447e1711bc221e122f7c

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Citations in the corpus

A CLASS OF NONHOLOMORPHIC MODULAR FORMS II: EQUIVARIANT ITERATED EISENSTEIN INTEGRALS (2017, background): “e subalgebra ls= M r≥1 pls∩Q[x1,...,xr] of solutions to linearised double shuﬄe equations in polynomials (i.e., with no poles) is related to the structure of depth-graded motivic multiple zeta values [22, 5]. It follows from theorem 12.1 that the structure of MIE is intimately connected to the struc”