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

Charlton, Steven

Authors

Steven Charlton



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
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.
Related Public URLs http://arxiv.org/abs/1306.6775

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