Bounds for double zeta-functions

Isao Kiuchi; Yoshio Tanigawa

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (2006)

  • Volume: 5, Issue: 4, page 445-464
  • ISSN: 0391-173X

Abstract

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In this paper we shall derive the order of magnitude for the double zeta-functionof Euler-Zagier type in the region 0 ≤ ℜ s j < 1 ( j = 1 , 2 ) .First we prepare the Euler-Maclaurinsummation formula in a suitable form for our purpose, and then we apply the theory of doubleexponential sums of van der Corput’s type.

How to cite

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Kiuchi, Isao, and Tanigawa, Yoshio. "Bounds for double zeta-functions." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 5.4 (2006): 445-464. <http://eudml.org/doc/239607>.

@article{Kiuchi2006,
abstract = {In this paper we shall derive the order of magnitude for the double zeta-functionof Euler-Zagier type in the region $0 \le \Re s_j &lt;1 \ \ (j=1,2)$.First we prepare the Euler-Maclaurinsummation formula in a suitable form for our purpose, and then we apply the theory of doubleexponential sums of van der Corput’s type.},
author = {Kiuchi, Isao, Tanigawa, Yoshio},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
language = {eng},
number = {4},
pages = {445-464},
publisher = {Scuola Normale Superiore, Pisa},
title = {Bounds for double zeta-functions},
url = {http://eudml.org/doc/239607},
volume = {5},
year = {2006},
}

TY - JOUR
AU - Kiuchi, Isao
AU - Tanigawa, Yoshio
TI - Bounds for double zeta-functions
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 2006
PB - Scuola Normale Superiore, Pisa
VL - 5
IS - 4
SP - 445
EP - 464
AB - In this paper we shall derive the order of magnitude for the double zeta-functionof Euler-Zagier type in the region $0 \le \Re s_j &lt;1 \ \ (j=1,2)$.First we prepare the Euler-Maclaurinsummation formula in a suitable form for our purpose, and then we apply the theory of doubleexponential sums of van der Corput’s type.
LA - eng
UR - http://eudml.org/doc/239607
ER -

References

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  13. [13] K. Matsumoto, On the analytic continuation of various multiple zeta-functions, In: “Number Theory for the Millennium, Proc. Millennial Conf. Number Theory”, Vol. II, M. A. Bennett et al. (eds.), A K Peters 2002, 417–440. Zbl1031.11051MR1956262
  14. [14] Y. Ohno, A generalization of the duality and sum formulas on the multiple zeta values, J. Number Theory 74 (1999), 39–43. Zbl0920.11063MR1670544
  15. [15] E. C. Titchmarsh, On Epstein’s zeta-function, Proc. London Math. Soc. (2) 36 (1934), 485–500. Zbl0008.30101
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  17. [17] J. Q. Zhao, Analytic continuation of multiple zeta function, Proc. Amer. Math. Soc. 128 (2000), 1275–1283. Zbl0949.11042MR1670846

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