The Analytic Continuation and the Asymptotic Behaviour of Certain Multiple Zeta-Functions(III)
The Analytic Continuation and the Asymptotic Behaviour of Certain Multiple Zeta-Functions(III)
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DOI：
10.1016/s0022-314x(03)00041-6
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发表时间：
2003-08
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影响因子：
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通讯作者：
Kohji Matsumoto
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文献类型：
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作者：
Kohji Matsumoto
我们考虑一般的多元多重zeta函数，包括巴恩斯多重zeta函数和Euler-Zagier和作为特例.我们证明了亚纯延拓到整个空间，渐近展开，和上界估计。这些结果有望应用于某些算术L-函数（如Hecke和Shintani的L-函数）。该方法基于经典的Mellin-Barnes积分公式。
We consider general multiple zeta-functions of multi-variables, including both Barnes multiple zeta-functions and Euler–Zagier sums as special cases. We prove the meromorphic continuation to the whole space, asymptotic expansions, and upper bound estimates. These results are expected to have applications to some arithmetical L-functions (such as of Hecke and of Shintani). The method is based on the classical Mellin–Barnes integral formula.