Abstract
We prove upper bound estimates for Euler-Zagier multiple zeta-functions. First, by shifting the paths of the relevant Mellin-Barnes type integrals to the right, we prove an estimate for general $r$-fold zeta-functions. Then, in the cases $r=2$ and $r=3$, we give further improvements by shifting the path suitably to the left.
Citation
Hideaki Ishikawa. Kohji Matsumoto. "On the estimation of the order of Euler-Zagier multiple zeta-functions." Illinois J. Math. 47 (4) 1151 - 1166, Winter 2003. https://doi.org/10.1215/ijm/1258138096
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