A t-motivic interpretation of shuffle relations for multizeta values

JOURNAL OF NUMBER THEORY

卷:232

Article

Huang, Wei-Cheng¹ 

[1] Texas A&M Univ, Dept Math, College Stn, TX 77843 USA

关键词: Multizeta values;    Shuffle relations;    t-modules;   

DOI  :  10.1016/j.jnt.2019.05.010

来源: Elsevier

【 摘 要 】

Thakur [Tha10] showed that, for r, s is an element of N, a product of two Carlitz zeta values zeta A(r) and zeta A(s) can be expressed as an Fp-linear combination of zeta A(r + s) and double zeta values of weight r + s. Such an expression is called shuffle relation by Thakur. Fixing r, s is an element of N, we construct a t-module E'. To determine whether an (r + s)-tuple C in Fq(theta)r+s gives a shuffle relation, we relate it to the Fq[t]-torsion property of the point vC is an element of E'(Fq[theta]) constructed with respect to the given (r +s)-tuple C. We also provide an effective criterion for deciding the Fq[t]-torsion property of the point vC. (c) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free