Depth-graded motivic multiple zeta values

2013/01/14 by Brown, Francis · 5 citations
#11M32 #13B05 #16T05 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1301.3053

Abstract

We study the depth filtration on multiple zeta values, the motivic Galois group of mixed Tate motives over ℤ and the Grothendieck-Teichmüller group, and its relation to modular forms. Using period polynomials for cusp forms for SL₂(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 ζ(2) and modulo lower depth. We formulate a single conjecture about the homology of this Lie algebra which implies conjectures due to Broadhurst-Kreimer, Racinet, Zagier and Drinfeld on the structure of multiple zeta values and on the Grothendieck-Teichmüller Lie algebra.

Cited by

• Numerical computation of linearized KV and the Deligne-Drinfeld and Broadhurst-Kreimer conjectures
• An extension of the linearized double shuffle Lie algebra
• On a proof of Xu's Conjecture and depths of Galois descents
• An explicit parity theorem for multiple polylogarithms
• Solving Infinite Families of Dual Conformal Integrals and Periods

Related

• The depth structure of motivic multiple zeta values
• Zeta elements in depth 3 and the fundamental Lie algebra of a punctured elliptic curve
• The motivic Galois group for a double zeta value
• Anatomy of an associator
• Relating depth graded and block graded motivic Lie algebras