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Volumn 101, Issue 2, 2003, Pages 223-243

The analytic continuation and the asymptotic behavior of certain multiple zeta-functions I

Author keywords

Analytic continuation; Asymptotic expansion; Mellin Barnes formula; Multiple zeta function

Indexed keywords


EID: 0041704854     PISSN: 0022314X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0022-314X(03)00041-6     Document Type: Article
Times cited : (70)

References (16)
  • 1
    • 0035651776 scopus 로고    scopus 로고
    • An analytic continuation of multiple zeta functions and their values at non-positive integers
    • S. Akiyama, S. Egami, Y. Tanigawa, An analytic continuation of multiple zeta functions and their values at non-positive integers, Acta Arith. 98 (2001) 107-116.
    • (2001) Acta Arith. , vol.98 , pp. 107-116
    • Akiyama, S.1    Egami, S.2    Tanigawa, Y.3
  • 2
    • 0041489182 scopus 로고    scopus 로고
    • On analytic continuation of multiple L-functions and related zeta-functions
    • C. Jia, K. Matsumoto (Eds.), Kluwer Academic Publishers, Dordrecht
    • S. Akiyama, H. Ishikawa, On analytic continuation of multiple L-functions and related zeta-functions, in: C. Jia, K. Matsumoto (Eds.), Analytic Number Theory, Developments in Mathematics, Vol. 6, Kluwer Academic Publishers, Dordrecht, 2002, pp. 1-16.
    • (2002) Analytic Number Theory, Developments in Mathematics , vol.6 , pp. 1-16
    • Akiyama, S.1    Ishikawa, H.2
  • 3
    • 0001153313 scopus 로고    scopus 로고
    • Multiple zeta values, poly-Bernoulli numbers, and related zeta functions
    • T. Arakawa, M. Kaneko, Multiple zeta values, poly-Bernoulli numbers, and related zeta functions, Nagoya Math. J. 153 (1999) 189-209.
    • (1999) Nagoya Math. J. , vol.153 , pp. 189-209
    • Arakawa, T.1    Kaneko, M.2
  • 4
    • 0000457764 scopus 로고
    • On the theory of multiple gamma function
    • E.W. Barnes, On the theory of multiple gamma function, Trans. Cambridge Philos. Soc. 19 (1904) 374-425.
    • (1904) Trans. Cambridge Philos. Soc. , vol.19 , pp. 374-425
    • Barnes, E.W.1
  • 5
    • 0003648303 scopus 로고
    • London Mathematical Society Student Texts, Cambridge University Press, Cambridge
    • H. Hida, Elementary Theory of L-functions and Eisenstein Series, London Mathematical Society Student Texts, Vol. 26, Cambridge University Press, Cambridge, 1993.
    • (1993) Elementary Theory of L-functions and Eisenstein Series , vol.26
    • Hida, H.1
  • 7
    • 0000905880 scopus 로고    scopus 로고
    • An application of Mellin-Barnes' type integrals to the mean square of Lerch zeta-functions
    • M. Katsurada, An application of Mellin-Barnes' type integrals to the mean square of Lerch zeta-functions, Collect. Math. 48 (1997) 137-153.
    • (1997) Collect. Math. , vol.48 , pp. 137-153
    • Katsurada, M.1
  • 8
    • 54649084734 scopus 로고    scopus 로고
    • An application of Mellin-Barnes type of integrals to the mean square of L-functions
    • Lithuanian Math. J. 38 (1998) 77-88
    • M. Katsurada, An application of Mellin-Barnes type of integrals to the mean square of L-functions, Liet. Mat. Rink. 38 (1998) 98-112; Lithuanian Math. J. 38 (1998) 77-88.
    • (1998) Liet. Mat. Rink. , vol.38 , pp. 98-112
    • Katsurada, M.1
  • 9
    • 21444440398 scopus 로고    scopus 로고
    • Explicit formulas and asymptotic expansions for certain mean square of Hurwitz zeta-functions I
    • M. Katsurada, K. Matsumoto, Explicit formulas and asymptotic expansions for certain mean square of Hurwitz zeta-functions I, Math. Scand. 78 (1996) 161-177.
    • (1996) Math. Scand. , vol.78 , pp. 161-177
    • Katsurada, M.1    Matsumoto, K.2
  • 10
    • 85022840222 scopus 로고    scopus 로고
    • Asymptotic series for double zeta, double gamma, and Hecke L-functions
    • Corrigendum and addendum, Math. Proc. Cambridge Philos. Soc. 132 (2002) 377-384
    • K. Matsumoto, Asymptotic series for double zeta, double gamma, and Hecke L-functions, Math. Proc. Cambridge Philos. Soc. 123 (1998) 385-405; Corrigendum and addendum, Math. Proc. Cambridge Philos. Soc. 132 (2002) 377-384.
    • (1998) Math. Proc. Cambridge Philos. Soc. , vol.123 , pp. 385-405
    • Matsumoto, K.1
  • 11
    • 85009849142 scopus 로고    scopus 로고
    • Asymptotic expansions of double zeta-functions of Barnes, of Shintani, and Eisenstein series
    • to appear
    • K. Matsumoto, Asymptotic expansions of double zeta-functions of Barnes, of Shintani, and Eisenstein series, Nagoya Math. J., to appear.
    • Nagoya Math. J.
    • Matsumoto, K.1
  • 12
    • 0042991785 scopus 로고    scopus 로고
    • Asymptotic expansions of double gamma-functions and related remarks
    • C. Jia, K. Matsumoto (Eds.), Kluwer Academic Publishers, Dordrecht
    • K. Matsumoto, Asymptotic expansions of double gamma-functions and related remarks, in: C. Jia, K. Matsumoto (Eds.), Analytic Number Theory, Developments in Mathematics, Vol. 6, Kluwer Academic Publishers, Dordrecht, 2002, pp. 243-268.
    • (2002) Analytic Number Theory, Developments in Mathematics , vol.6 , pp. 243-268
    • Matsumoto, K.1
  • 13
    • 85201598519 scopus 로고    scopus 로고
    • On the analytic continuation of various multiple zeta-functions
    • M.A. Bennett et al. (Eds.), Proc. Millennial Conference on Number Theory, A K Peters, Wellesley
    • K. Matsumoto, On the analytic continuation of various multiple zeta-functions, in: M.A. Bennett et al. (Eds.), Number Theory for the Millennium II, Proc. Millennial Conference on Number Theory, A K Peters, Wellesley, 2002, pp. 417-440.
    • (2002) Number Theory for the Millennium II , pp. 417-440
    • Matsumoto, K.1
  • 15
    • 0000507256 scopus 로고
    • Values of zeta functions and their applications
    • A. Joseph et al. (Eds.), Invited Lectures Progress in Mathematics, Vol. 120, Birkhäuser, Basel
    • D. Zagier, Values of zeta functions and their applications, in: A. Joseph et al. (Eds.), First European Congress of Mathematics, Vol. II, Invited Lectures (Part 2), Progress in Mathematics, Vol. 120, Birkhäuser, 1994, Basel, pp. 497-512.
    • (1994) First European Congress of Mathematics , vol.2 , Issue.PART 2 , pp. 497-512
    • Zagier, D.1
  • 16
    • 23044520708 scopus 로고    scopus 로고
    • Analytic continuation of multiple zeta functions
    • J. Zhao, Analytic continuation of multiple zeta functions, Proc. Amer. Math. Soc. 128 (2000) 1275-1283.
    • (2000) Proc. Amer. Math. Soc. , vol.128 , pp. 1275-1283
    • Zhao, J.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.