RESTRICTED SUM FORMULA FOR FINITE AND SYMMETRIC MULTIPLE ZETA VALUES

被引：2

作者：

Murahara, Hideki ^{[1
]}

Saito, Shingo ^{[2
]}

机构：

[1] Nakamura Gakuen Univ, Grad Sch, Jonan Ku, Fukuoka, Fukuoka, Japan

[2] Kyushu Univ, Fac Arts & Sci, Nishi Ku, Fukuoka, Fukuoka, Japan

来源：

PACIFIC JOURNAL OF MATHEMATICS | 2019年 / 303卷 / 01期

基金：

日本学术振兴会;

关键词：

finite multiple zeta values; symmetric multiple zeta values; symmetrised multiple zeta values; finite real multiple zeta values; sum formula; restricted sum formula;

D O I：

10.2140/pjm.2019.303.325

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The sum formula for finite and symmetric multiple zeta values, established by Wakabayashi and the authors, implies that if the weight and depth are fixed and the specified component is required to be more than one, then the values sum up to a rational multiple of the analogue of the Riemann zeta value. We prove that the result remains true if we further demand that the component should be more than two or that another component should also be more than one.

引用

页码：325 / 335

页数：11

共 50 条

[21] A Weighted Sum Formula for Alternating Multiple Zeta-Star Values
Gencev, Marian
MEDITERRANEAN JOURNAL OF MATHEMATICS, 2021, 18 (06)
[22] Finite and symmetric Mordell-Tornheim multiple zeta values
Bachmann, Henrik
Takeyama, Yoshihiro
Tasaka, Koji
JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN, 2021, 73 (04) : 1129 - 1158
[23] Sum formula for multiple zeta function
Hirose, Minoru
Murahara, Hideki
Onozuka, Tomokazu
RAMANUJAN JOURNAL, 2024, 65 (04): : 1607 - 1619
[24] Cyclic sum of multiple zeta values
Ohno, Yasuo
Wakabayashi, Noriko
ACTA ARITHMETICA, 2006, 123 (03) : 289 - 295
[25] Sum relations for multiple zeta values
Ohno, Y
ZETA FUNCTIONS, TOPOLOGY AND QUANTUM PHYSICS, 2005, 14 : 131 - 144
[26] Some restricted sum formulas for double zeta values
Machide, Tomoya
PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES, 2013, 89 (03) : 51 - 54
[27] On multiple zeta values and finite multiple zeta values of maximal height
Murahara, Hideki
Sakata, Mika
INTERNATIONAL JOURNAL OF NUMBER THEORY, 2018, 14 (04) : 975 - 987
[28] FINITE MULTIPLE ZETA VALUES, SYMMETRICMULTIPLE ZETA VALUES AND UNIFIED MULTIPLE ZETA FUNCTIONS
Komori, Yasushi
TOHOKU MATHEMATICAL JOURNAL, 2021, 73 (02) : 221 - 255
[29] On the sum formula for the q-analogue of non-strict multiple zeta values
Ohno, Yasuo
Okuda, Jun-Ichi
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2007, 135 (10) : 3029 - 3037
[30] SYMMETRIC FUNCTIONS AND MULTIPLE ZETA VALUES
Chu, Wenchang
BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 2020, 101 (03) : 426 - 437

← 1 2 3 4 5 →