Analytic properties of multiple zeta functions and certain weighted variants, an elementary approach

详细信息    查看全文

• 作者：Jay Mehta ^{jaymehta@imsc.res.in" class="auth_mail" title="E-mail the corresponding author} ; Biswajyoti Saha ; ^{biswajyoti@imsc.res.in" class="auth_mail" title="E-mail the corresponding author} ; G.K. Viswanadham ^{viswanadh@imsc.res.in" class="auth_mail" title="E-mail the corresponding author}
• 关键词：11M32
• 刊名：Journal of Number Theory
• 出版年：2016
• 出版时间：November 2016
• 年：2016
• 卷：168
• 期：Complete
• 页码：487-508
• 全文大小：462 K

文摘

In this article we obtain the meromorphic continuation of multiple zeta functions, together with a complete list of their poles and residues, by means of an elementary and simple translation formula for these multiple zeta functions. The use of matrices to express this translation formula leads, in particular, to a succinct description of the residues of the multiple zeta functions. We conclude our paper by introducing certain interesting weighted variants of multiple zeta functions. They are shown to behave particularly nicely with respect to product formulas and location of poles.