Analytic Continuation of Multiple Zeta Functions

@inproceedings{Zhao1999AnalyticCO,
  title={Analytic Continuation of Multiple Zeta Functions},
  author={Jianqiang Zhao},
  year={1999}
}
In this paper we shall define the analytic continuation of the multiple (Euler-Riemann-Zagier) zeta functions of depth d: ζ(s1, . . . , sd) := ∑ 0<n1<n2<···<nd 1 n1 1 n s2 2 · · ·n sd d , where Re (sd) > 1 and ∑d j=1 Re (sj) > d. We shall also study their behavior near the poles and pose some open problems concerning their zeros and functional equations at the end. 
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Showing 1-10 of 10 references

Meditationes circa singvlare seriervm genus

  • L. Euler
  • Novi Comm. Acad. Sci. Petropol 20
  • 1775
Highly Influential
6 Excerpts

Explicit evaluation of Euler sums

  • D. Borwein, J. M. Borwein, R. Girgensohn
  • Proc. Edinburgh Math. Soc. 38
  • 1995
1 Excerpt

Interpretation motivique de la conjecture de Zagier

  • A. A. Beilinson, P. Deligne
  • in: Symp. in Pure Math. vol. 55, part 2
  • 1994
1 Excerpt

MR 95 a : 19008 [ 5 ] L . Euler , Meditationes circa singvlare seriervm genus , Novi Comm

  • G. E. Shilov
  • Acad . Sci . Petropol
  • 1994

Values of zeta functions and their applications

  • D. Zagier
  • in: Proc. of the First European Congress of Math…
  • 1992
1 Excerpt

Multiple zeta functions: an example

  • N. Kurokawa
  • in: Zeta Functions in Geometry,
  • 1990

Polylogarithms

  • D. Zagier
  • Dedekind zeta functions, and the algebraic K…
  • 1989
1 Excerpt

Dirichlet series related to the Riemann zeta function

  • T. M. Apostol, T. H. Vu
  • J. of Number Theory 19
  • 1984
1 Excerpt

Generalized Functions vol

  • I. M. Gelfand, G. E. Shilov
  • I, Academic Press, New York, London
  • 1964
2 Excerpts

Kontsevich integral for the Homely polynomial and relations between values of multiple zeta functions , Topology and Appl

  • J. Murakami

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