On the estimation of the order of Euler-Zagier multiple zeta-functions
Ishikawa, Hideaki ; Matsumoto, Kohji
Illinois J. Math., Tome 47 (2003) no. 4, p. 1151-1166 / Harvested from Project Euclid
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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.
Publié le : 2003-10-15
Classification:  11M41 
@article{1258138096,
     author = {Ishikawa, Hideaki and Matsumoto, Kohji},
     title = {On the estimation of the order of Euler-Zagier multiple zeta-functions},
     journal = {Illinois J. Math.},
     volume = {47},
     number = {4},
     year = {2003},
     pages = { 1151-1166},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1258138096}
}

Ishikawa, Hideaki; Matsumoto, Kohji. On the estimation of the order of Euler-Zagier multiple zeta-functions. Illinois J. Math., Tome 47 (2003) no. 4, pp.  1151-1166. http://gdmltest.u-ga.fr/item/1258138096/