Mixed Tate motives and multiple zeta values

By T. Terasoma. 2001

180 citations recorded by the source corpus.

In this paper, we construct an object of the abelian category of mixed Tate motive associated to multiple zeta values. as a consequence, we prove the inequality of the dimension of the vector space generated by multiple zeta values, which is conjectured by Zagier. (Some errors was corrected from the first version. Namely, we changed the definition of the boundary $\bold B^0$.)

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/3494b873db9f0303dc1b1c92f753467c417b09ac

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Geometry and Topology

1. Bin Zhang
2. F. Brown
3. J. Okuda
4. K. Ihara
5. Don Zagier
6. Li Guo
7. Jeffrey C. Lagarias
8. Michael E. Hoffman

In Mathematical Physics

1. F. Brown
2. Li Guo
3. Jeffrey C. Lagarias
4. Don Zagier
5. Michael E. Hoffman
6. Bin Zhang
7. K. Ihara
8. J. Okuda

Citations in the corpus

• QUASI-SYMMETRIC FUNCTIONS AND MOD p MULTIPLE HARMONIC SUMS (2004, background): “It has been proved by T. Terasoma [28] and A. B. Goncharov [10] that the true dimension of this rational vector space is at most dn.”
• Evaluation of the multiple zeta values $\zeta(2,\dots,2,3,2,\dots,2)$ (2012, methodology): “) However, the true MZV’s in R are the images under a Q-linear map of certain “motivic” MZV’s which are defined purely algebraically, and it was proved (independently) by Terasoma [10] and Goncharov [6], [3] that the upper bound implied by the conjectural dimension formula held for these, implying i”
• On the decomposition of motivic multiple zeta values (2011, methodology): “This theorem was first proved independently by Goncharov (see Deligne-Goncharov [4]) and Terasoma [8].”
• On relations for the multiple q-zeta values (2007, background): “In fact, the following equality holds up to q269: 4ζ[7, 2] + 6ζ[6, 3]− ζ[5, 4]− ζ[4, 5]− 6ζ[6, 2, 1]− 6ζ[6, 1, 2] −2ζ[5, 3, 1]− 7ζ[5, 2, 2]− 3ζ[5, 1, 3] + 2ζ[4, 4, 1]− ζ[4, 3, 2] +ζ[3, 5, 1] + ζ[3, 2, 4]− 3ζ[2, 5, 2] + 2ζ[5, 2, 1, 1] +2ζ[5, 1, 2, 1] + 2ζ[5, 1, 1, 2] + ζ[3, 3, 1, 2]− ζ[3, 2, 3, 1] −4”
• New properties of multiple harmonic sums modulo $p$ and $p$-analogues of Leshchiner's series (2012, unknown): “T. Terasoma, Mixed Tate motives and multiple zeta values, Invent.”
• Derivation and double shuffle relations for multiple zeta values (2006, background): “This conjecture is still open, but it has been shown by Terasoma [16] and independently by Goncharov [5] that the coefficient of x in (1−x2−x3)−1 is an upper bound for dimZk.”
• Renormalization of multiple zeta values (2006, background): “Since then MZVs and their generalizations have been studied extensively by numerous authors from different point of views with connections to arithmetic geometry, mathematical physics, quantum groups and knot theory [5, 8, 11, 23, 24, 32, 34, 42].”
• Euler's constant: Euler's work and modern developments (2013, background): “Terasoma [297], [298] and Deligne and Goncharov [66].”