ON MULTIPLE ZETA VALUES OF LEVEL TWO

被引：24

作者：

Kaneko, Masanobu ^{[1
]}

Tsumura, Hirofumi ^{[2
]}

机构：

[1] Kyushu Univ, Fac Math, Nishi Ku, Motooka 744, Fukuoka 8190395, Japan

[2] Tokyo Metropolitan Univ, Dept Math Sci, 1-1 Minami Ohsawa, Hachioji, Tokyo 1920397, Japan

来源：

TSUKUBA JOURNAL OF MATHEMATICS | 2020年 / 44卷 / 02期

基金：

日本学术振兴会;

关键词：

Multiple zeta values; polylogarithms; inverse trigonometric functions; DOUBLE SHUFFLE RELATIONS; POLY-BERNOULLI NUMBERS;

D O I：

10.21099/tkbjm/20204402213

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study a variant of multiple zeta values of level 2, which forms a subspace of the space of alternating multiple zeta values. This variant, which is regarded as the 'shuffle counterpart' of Homan's 'odd variant', exhibits nice properties such as duality, shuffle product, parity results, etc., like ordinary multiple zeta values. We also give some conjectures on relations between our values, Hoffman's values, and multiple zeta values.

引用

页码：213 / 234

页数：22

共 21 条

[1] SPECIAL VALUES OF HYPERLOGARITHMS AND LINEAR DIFFERENCE-SCHEMES
AOMOTO, K
[J]. ILLINOIS JOURNAL OF MATHEMATICS, 1990, 34 (02) : 191 - 216
[2] Multiple zeta values, poly-Bernoulli numbers, and related zeta functions
Arakawa, T
Kaneko, M
[J]. NAGOYA MATHEMATICAL JOURNAL, 1999, 153 : 189 - 209
[3] EXPLICIT EVALUATION OF EULER SUMS
BORWEIN, D
BORWEIN, JM
GIRGENSOHN, R
[J]. PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY, 1995, 38 : 277 - 294
[4] Drinfeld V.G., 1990, Algebra Anal, P829
[5] Double zeta values and modular forms
Gangl, H
Kaneko, M
Zagier, D
[J]. AUTOMORPHIC FORMS AND ZETA FUNCTIONS, 2006, : 71 - +
[6] Glanois, ARXIV160305178
[7] Hoffman ME, 2019, COMMUN NUMBER THEORY, V13, P529
[8] Derivation and double shuffle relations for multiple zeta values
Ihara, K
Kaneko, M
Zagier, D
[J]. COMPOSITIO MATHEMATICA, 2006, 142 (02) : 307 - 338
[9] Kaneko M., 2020, ADV STUD PURE MATH, V84, P181, DOI DOI 10.2969/ASPM/08410181
[10] Kaneko M, 2013, MATH ANN, V357, P1091, DOI 10.1007/s00208-013-0930-5

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