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ON MULTIPLE ZETA VALUES OF EXTREMAL HEIGHT

Part of: Zeta and $L$-functions: analytic theory

Published online by Cambridge University Press:  11 November 2015

MASANOBU KANEKO  and
MIKA SAKATA
MASANOBU KANEKO
Affiliation:
Faculty of Mathematics, Kyushu University, Motooka 744, Nishi-ku, Fukuoka 819-0395, Japan email mkaneko@math.kyushu-u.ac.jp
MIKA SAKATA*
Affiliation:
Graduate School of Mathematics, Kyushu University, Motooka 744, Nishi-ku, Fukuoka 819-0395, Japan email m-sakata@math.kyushu-u.ac.jp
*
✉m-sakata@math.kyushu-u.ac.jp
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Abstract

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We give three identities involving multiple zeta values of height one and of maximal height: an explicit formula for the height-one multiple zeta values, a regularised sum formula and a sum formula for the multiple zeta values of maximal height.

Keywords

multiple zeta valuesArakawa–Kaneko zeta function

MSC classification

Primary: 11M32: Multiple Dirichlet series and zeta functions and multizeta values
Secondary: 11M41: Other Dirichlet series and zeta functions
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 93 , Issue 2 , April 2016 , pp. 186 - 193
Copyright
© 2015 Australian Mathematical Publishing Association Inc. 

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