Dans cet article, nous considérons que certaines séries de Dirichlet multiples, dont nous montrons le prolongement analytique en utilisant la formule intégrale de Mellin-Barnes. Des majorations de ces séries sont également obtenues.
Multiple Dirichlet series of several complex variables are considered. Using the Mellin-Barnes integral formula, we prove the analytic continuation and an upper bound estimate.
@article{JTNB_2003__15_1_267_0,
author = {Kohji Matsumoto and Yoshio Tanigawa},
title = {The analytic continuation and the order estimate of multiple {Dirichlet} series},
journal = {Journal de th\'eorie des nombres de Bordeaux},
pages = {267--274},
publisher = {Universit\'e Bordeaux I},
volume = {15},
number = {1},
year = {2003},
zbl = {1050.11082},
mrnumber = {2019016},
language = {en},
url = {https://jtnb.centre-mersenne.org/item/JTNB_2003__15_1_267_0/}
}
TY - JOUR AU - Kohji Matsumoto AU - Yoshio Tanigawa TI - The analytic continuation and the order estimate of multiple Dirichlet series JO - Journal de théorie des nombres de Bordeaux PY - 2003 SP - 267 EP - 274 VL - 15 IS - 1 PB - Université Bordeaux I UR - https://jtnb.centre-mersenne.org/item/JTNB_2003__15_1_267_0/ LA - en ID - JTNB_2003__15_1_267_0 ER -
%0 Journal Article %A Kohji Matsumoto %A Yoshio Tanigawa %T The analytic continuation and the order estimate of multiple Dirichlet series %J Journal de théorie des nombres de Bordeaux %D 2003 %P 267-274 %V 15 %N 1 %I Université Bordeaux I %U https://jtnb.centre-mersenne.org/item/JTNB_2003__15_1_267_0/ %G en %F JTNB_2003__15_1_267_0
Kohji Matsumoto; Yoshio Tanigawa. The analytic continuation and the order estimate of multiple Dirichlet series. Journal de théorie des nombres de Bordeaux, Tome 15 (2003) no. 1, pp. 267-274. https://jtnb.centre-mersenne.org/item/JTNB_2003__15_1_267_0/
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