TY - JOUR

T1 - Bowman-bradley type theorem for finite multiple zeta values in A2

AU - Murahara, Hideki

AU - Onozuka, Tomokazu

AU - Seki, Shin Ichiro

N1 - Funding Information:
2010 Mathematics Subject Classification. 11M32. The third author is supported in part by the Grant-in-Aid for JSPS Fellows (JP18J00151), The Ministry of Education, Culture, Sports, Science and Technology, Japan.
Publisher Copyright:
© 2020, Osaka University. All rights reserved.

PY - 2020

Y1 - 2020

N2 - Bowman and Bradley obtained a remarkable formula among multiple zeta values. The formula states that the sum of multiple zeta values for indices which consist of the shuffle of two kinds of the strings {1, 3, …, 1, 3} and {2, …, 2} is a rational multiple of a power of π2. Recently, Saito and Wakabayashi proved that analogous but more general sums of finite multiple zeta values in an adelic ring1 vanish. In this paper, we partially lift Saito-Wakabayashi’s theorem from1 to2. Our result states that a Bowman-Bradley type sum of finite multiple zeta values in2 is a rational multiple of a special element and this is closer to the original Bowman-Bradley theorem.

AB - Bowman and Bradley obtained a remarkable formula among multiple zeta values. The formula states that the sum of multiple zeta values for indices which consist of the shuffle of two kinds of the strings {1, 3, …, 1, 3} and {2, …, 2} is a rational multiple of a power of π2. Recently, Saito and Wakabayashi proved that analogous but more general sums of finite multiple zeta values in an adelic ring1 vanish. In this paper, we partially lift Saito-Wakabayashi’s theorem from1 to2. Our result states that a Bowman-Bradley type sum of finite multiple zeta values in2 is a rational multiple of a special element and this is closer to the original Bowman-Bradley theorem.

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M3 - Article

AN - SCOPUS:85087845517

VL - 57

SP - 647

EP - 653

JO - Osaka Journal of Mathematics

JF - Osaka Journal of Mathematics

SN - 0030-6126

IS - 3

ER -