A note on linear independence of polylogarithms over the rationals

Proceedings of the Japan Academy, Series A. Mathematical Sciences

article

Noriko Hirata-Kohno¹  Hironori Okada² 

[1] Department of Mathematics, College of Science and Technology, Nihon University;Hozen High School

关键词: Polylogarithms;    Pade´ approximation;    irrationality;    linear independence.;   

DOI  :  10.3792/pjaa.88.156

学科分类：数学（综合）

来源: Japan Academy

【 摘 要 】

In this article, we give a new lower bound for the dimension of the linear space over the rationals spanned by 1 and values of polylogarithmic functions at a non-zero rational number. Our proof uses Padé approximation following the argument of T. Rivoal, however we adapt a new linear independence criterion due to S. Fischler and W. Zudilin. We also present an example of the linear space of dimension $\geqslant 3$ over $\mathbf{Q}$, which is generated by 1 and polylogarithms.

【 授权许可】

Unknown