ζ({{2}^m, 1, {2}^m, 3}^n, {2}^m) / π^(4n+2m(2n+1))) is rational

Charlton, Steven

Abstract

The cyclic insertion conjecture of Borwein, Bradley, Broadhurst and Lisoněk states that inserting all cyclic shifts of some fixed blocks of 2's into the multiple zeta value ζ(1,3,…,1,3) gives an explicit rational multiple of a power of π . In this paper we use motivic multiple zeta values to establish a non-explicit symmetric insertion result: inserting all possible permutations of some fixed blocks of 2's into ζ(1,3,…,1,3) gives some rational multiple of a power of π.

Citation

Charlton, S. (2015). ζ({{2}^m, 1, {2}^m, 3}^n, {2}^m) / π^(4n+2m(2n+1))) is rational. Journal of Number Theory, 148, 463-477. https://doi.org/10.1016/j.jnt.2014.09.028

• Journal Article Type: Article
• Acceptance Date: Sep 22, 2014
• Publication Date: Mar 1, 2015
• Deposit Date: Aug 27, 2015
• Publicly Available Date: Sep 4, 2015
• Journal: Journal of Number Theory
• Print ISSN: 0022-314X
• Electronic ISSN: 1096-1658
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 148
• Pages: 463-477
• DOI: https://doi.org/10.1016/j.jnt.2014.09.028
• Keywords: Multiple zeta values, Motivic multiple zeta values, Cyclic insertion conjecture.
• Public URL: https://durham-repository.worktribe.com/output/1423715
• Related Public URLs: http://arxiv.org/abs/1306.6775