Vol. 257, No. 2, 2012

Download this article
Download this article. For screen
For printing
Recent Issues
Vol. 269: 1
Vol. 268: 1  2
Vol. 267: 1  2
Vol. 266: 1  2
Vol. 265: 1  2
Vol. 264: 1  2
Vol. 263: 1  2
Vol. 262: 1  2
Online Archive
Volume:
Issue:
     
The Journal
Editorial Board
Officers
Special Issues
Submission Guidelines
Submission Form
Subscriptions
Contacts
Author Index
To Appear
 
ISSN: 0030-8730
On a conjecture of Kaneko and Ohno

Zhong-hua Li

Vol. 257 (2012), No. 2, 419–430
Abstract

Let X0(k,n,s) denote the sum of all multiple zeta-star values of weight k, depth n and height s. Kaneko and Ohno conjectured that, for any positive integers m,n,s with m,n s, the difference

(− 1)mX ⋆0(m+n+1, n+1, s)− (− 1)nX⋆0(m+n+1, m+1,  s)

can be expressed as a polynomial of zeta values with rational coefficients. We give a proof of this conjecture.

Keywords
multiple zeta-star values, generalized hypergeometric function
Mathematical Subject Classification 2010
Primary: 11M32, 33C20
Milestones
Received: 27 June 2011
Accepted: 4 June 2012
Published: 4 July 2012
Authors
Zhong-hua Li
Department of Mathematics
Tongji University
No. 1239 Siping Road
Shanghai 200092
China
Graduate School of Mathematical Sciences
The University of Tokyo
3-8-1 Komaba, Meguro
Tokyo 153-8914
Japan