Finite and symmetrized colored multiple zeta values

Singer J, Zhao J (2020)

Publication Type: Journal article

Publication year: 2020

Journal

Finite Fields and Their Applications Elsevier

Book Volume: 65

Article Number: 101676

DOI: 10.1016/j.ffa.2020.101676

Abstract

Colored multiple zeta values are special values of multiple polylogarithms evaluated at Nth roots of unity. In this paper, we define both the symmetrized version of these values for all positive integers N and the finite version for N=3,4 and 6. We then show that both versions satisfy the double shuffle relations. Further, for N=3 and 4 we provide strong evidence for an isomorphism connecting the two spaces generated by these two kinds of values. This is a higher level analog of a recent work of Kaneko and Zagier on finite and symmetrized multiple zeta values at level one and of the second author on finite and symmetrized Euler sums at level two.

Authors with CRIS profile

Johannes Singer Lehrstuhl für Darstellungstheorie

Involved external institutions

The Bishop's School US United States (USA) (US)

How to cite

APA:

Singer, J., & Zhao, J. (2020). Finite and symmetrized colored multiple zeta values. Finite Fields and Their Applications, 65. https://dx.doi.org/10.1016/j.ffa.2020.101676

MLA:

Singer, Johannes, and Jianqiang Zhao. "Finite and symmetrized colored multiple zeta values." Finite Fields and Their Applications 65 (2020).

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