全部 标题 作者
关键词 摘要

OALib Journal期刊
ISSN: 2333-9721
费用:99美元

查看量下载量

相关文章

更多...
Mathematics  2008 

Generators for Vector Spaces Spanned by Double Zeta Values with Even Weight

DOI: 10.1016/j.jnt.2012.12.010

Full-Text   Cite this paper   Add to My Lib

Abstract:

Let $\mathcal{DZ}_k$ be the $\mathbb{Q}$-vector space spanned by double zeta values with weight $k$, and $\mathcal{DM}_k$ be its quotient space divided by the space $\mathcal{PZ}_k$ 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 $\mathcal{DM}_k$ is known. By adding the dimensions of $\mathcal{DM}_k$ and $\mathcal{PZ}_k$, an upper bound of $\mathcal{DZ}_k$ 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 $\mathcal{DM}_k$ which represent the upper bound. These yield the corresponding sets and the upper bound for $\mathcal{DZ}_k$.

Full-Text

Contact Us

service@oalib.com

QQ:3279437679

WhatsApp +8615387084133