Generators for vector spaces spanned by double zeta values with even weight

JOURNAL OF NUMBER THEORY

卷:133

Article

Machide, T.

关键词: Double zeta values;    Multiple zeta values;    Vector spaces spanned by double zeta values;    Generators;    Relations for double zeta values;    The vector space of modular forms;   

DOI  :  10.1016/j.jnt.2012.12.010

来源: Elsevier

【 摘 要 】

Let DZ(k) be the Q-vector space spanned by double zeta values with weight k, and DMk be its quotient space divided by the space PZ(k) spanned by the zeta value zeta(k) and products of two zeta values with total weight k. When k is even, an upper bound for the dimension of DMk is known. By adding the dimensions of DMk and PZ(k), an upper bound of DZ(k) which equals k/2 minus the dimension of the space of modular forms of weight k on the modular group is given. In this note, we obtain some specific sets of generators for DMk which represent the upper bound. These yield the corresponding sets and the upper bound for DZ(k). (C) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

Free