The analytic continuation and the order estimate of multiple Dirichlet series

Kohji Matsumoto; Yoshio Tanigawa

Journal de théorie des nombres de Bordeaux (2003)

  • Volume: 15, Issue: 1, page 267-274
  • ISSN: 1246-7405

Abstract

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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.

How to cite

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Matsumoto, Kohji, and Tanigawa, Yoshio. "The analytic continuation and the order estimate of multiple Dirichlet series." Journal de théorie des nombres de Bordeaux 15.1 (2003): 267-274. <http://eudml.org/doc/249090>.

@article{Matsumoto2003,
abstract = {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.},
author = {Matsumoto, Kohji, Tanigawa, Yoshio},
journal = {Journal de théorie des nombres de Bordeaux},
keywords = {multiple Dirichlet series},
language = {eng},
number = {1},
pages = {267-274},
publisher = {Université Bordeaux I},
title = {The analytic continuation and the order estimate of multiple Dirichlet series},
url = {http://eudml.org/doc/249090},
volume = {15},
year = {2003},
}

TY - JOUR
AU - Matsumoto, Kohji
AU - Tanigawa, Yoshio
TI - The analytic continuation and the order estimate of multiple Dirichlet series
JO - Journal de théorie des nombres de Bordeaux
PY - 2003
PB - Université Bordeaux I
VL - 15
IS - 1
SP - 267
EP - 274
AB - 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.
LA - eng
KW - multiple Dirichlet series
UR - http://eudml.org/doc/249090
ER -

References

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  9. [9] H. Ishikawa, A multiple character sum and a multiple L-function. Arch. Math.79 (2002), 439-448. Zbl1034.11053MR1967262
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  11. [11] K. Matsumoto, The analytic continuation and the asymptotic behaviour of certain multiple zeta-functions I. J. Number Theory, to appear. Zbl1083.11057MR1989886
  12. [12] K. Matsumoto, The analytic continuation and the asymptotic behaviour of certain multiple zeta-functions II. In: Analytic and Probabilistic Methods in Number Theory, Proc. 3rd Intern. Conf. in Honour of J. Kubilius (Palanga, Lithuania, Sept 2001), 188-194, A. Dubickas et al. (eds.), TEV, Vilnius, 2002. Zbl1195.11119MR1964862
  13. [13] J. Zhao, Analytic continuation of multiple zeta functions. Proc. Amer. Math. Soc.128 (2000), 1275-1283. Zbl0949.11042MR1670846

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