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Special Values of Zeta Functions Associated with Self-Dual Homogeneous Cones

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Manifolds and Lie Groups

Part of the book series: Progress in Mathematics ((PM,volume 14))

Abstract

To explain the main idea of this paper, and also to fix some notations, we start with reviewing the classical case of Riemann zeta function. As usual we set

$$\varsigma \left( s \right) = \sum\limits_{n = 1}^\infty {{n^{ - s}}} \quad \left( {Re\,s >1} \right)$$

,

$$\Gamma \left( s \right) = \int\limits_0^\infty {{x^{s - 1}}{e^{ - x}}dx\quad \left( {{\mathop{\rm Re}\nolimits} \,s >0} \right)}$$

.

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Author information

Authors and Affiliations

  1. University of California, Berkeley, California, 94720, USA

    I. Satake

  2. Tôhoku University, Sendai 980, Japan

    I. Satake

Authors
  1. I. Satake
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Editor information

Editors and Affiliations

  1. Department of Mathematics, Washington University, St. Louis, Missouri, 63130, USA

    Jun-ichi Hano

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© 1981 Springer Science+Business Media New York

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Satake, I. (1981). Special Values of Zeta Functions Associated with Self-Dual Homogeneous Cones. In: Hano, Ji., Morimoto, A., Murakami, S., Okamoto, K., Ozeki, H. (eds) Manifolds and Lie Groups. Progress in Mathematics, vol 14. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-5987-9_19

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  • DOI: https://doi.org/10.1007/978-1-4612-5987-9_19

  • Publisher Name: Birkhäuser, Boston, MA

  • Print ISBN: 978-1-4612-5989-3

  • Online ISBN: 978-1-4612-5987-9

  • eBook Packages: Springer Book Archive

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